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@INCOLLECTION{Adams2007,
  author = {Jeffrey Adams},
  title = {The Theta-Correspondence over R},
  booktitle = {HARMONIC ANALYSIS, GROUP REPRESENTATIONS, AUTOMORPHIC FORMS AND INVARIANT
	THEORY: In Honor of Roger E. Howe},
  publisher = {World Scientific Publishing Company},
  year = {2007},
  editor = {Jian-Shu Li, Eng-Chye Tan, Nolan Wallach, Chen-Bo Zhu},
  volume = {12},
  series = {Lecture Notes Series, Institute for Mathematical Sciences, National
	University of Singapore},
  month = {Nov},
  file = {:D\:\\eBooks\\papers\\representation\\Jeffrey Adams, The theta Correspondence over R.PDF:PDF},
  owner = {hoxide},
  timestamp = {2009.05.06}
}

@ARTICLE{Adams1989,
  author = {Adams, J.},
  title = {L-functoriality for dual pairs.},
  year = {1989},
  abstract = {{[For the entire collection see Zbl 0694.00012.] \par This paper considers
	the notion of functoriality for the correspondence given by the oscillator
	representation for a dual reductive pair $(G,G')$ in Sp(2n,${\bbfR})$,
	assuming the oscillator representation factors to $G\times G'.$ \par
	There are counterexamples to the obvious conjecture in terms of L-
	packets, so the author proposes using the larger packets called Arthur-
	packets. These packets are parametrized by admissible maps $\Psi$
	: $W\sb R\times SL(2,{\bbfC})\to\sp LG$. The conjecture is that given
	$G,G'$, there is (after possibly exchanging $G,G')$ a map $\gamma$
	: ${}\sp LG\to\sp LG'$ and a fixed homomorphism T: SL(2,${\bbfC})\to\sp
	LG'$, which describe the correspondence. \par The conjecture states
	that if a representation $\pi$ occurring in the correspondence is
	in the Arthur-packet determined by $\Psi$, then its image $\pi '$
	is in the Arthur-packet determined by $\Psi '(w,g)=\gamma \circ \Psi
	(w,g)T(g)$. The author proves this conjecture in many cases, showing
	it to be consistent with all known examples. There is also a conjecture
	concerning the correspondence not just between G and $G'$ but between
	all their inner forms.}},
  classmath = {{*22E47 (Repres. of Lie and real algebraic groups: algebraic methods)
	11S37 (Langlands-Weil conjectures, nonabelian class field theory)
	22E46 (Semi-simple Lie groups and their representations) }},
  howpublished = {{Orbites unipotentes et repr\'esentations. II: Groupes p-adiques
	et r\'eels, Ast\'erisque 171-172, 85-129 (1989).}},
  keywords = {{oscillator representation; dual reductive pair; L-packets; Arthur-
	packets; correspondence; inner forms}},
  language = {English},
  reviewer = {{J.Repka}}
}

@ARTICLE{Adams1987,
  author = {Jeffrey Adams},
  title = {Unitary highest weight modules},
  journal = {Advances in Mathematics},
  year = {1987},
  volume = {63},
  pages = {113 - 137},
  number = {2},
  doi = {DOI: 10.1016/0001-8708(87)90049-1},
  file = {:D\:\\eBooks\\papers\\representation\\Jeffrey Adams,Unitary highest weight modules.pdf:PDF},
  issn = {0001-8708},
  url = {http://www.sciencedirect.com/science/article/B6W9F-4CRY32C-NG/2/57342a474b890a540d1aadb816fcccd1}
}

@ARTICLE{Adams1987Co,
  author = {Jeffrey Adams},
  title = {Coadjoint orbits and reductive dual pairs},
  journal = {Advances in Mathematics},
  year = {1987},
  volume = {63},
  pages = {138 - 151},
  number = {2},
  doi = {DOI: 10.1016/0001-8708(87)90050-8},
  file = {:D\:\\eBooks\\papers\\representation\\Jeffery Adams, Coadjoint orbits and reductive dual pairs.pdf:PDF},
  issn = {0001-8708},
  url = {http://www.sciencedirect.com/science/article/B6W9F-4CRY32C-NH/2/7820a2edadd3d0aabece3f08bab8f8e5}
}

@ARTICLE{Adams1998,
  author = {ADAMS,JEFFREY and BARBASCH,DAN},
  title = {Genuine Representations of the Metaplectic Group},
  journal = {Compositio Mathematica},
  year = {1998},
  volume = {113},
  pages = {23-66},
  number = {01},
  abstract = {ABSTRACT This paper determines the &thgr;&ndash;correspondence for
	the dual pairs &lpar;O&lpar;p, q&rpar;, Sp&lpar;2n, R&rpar;&rpar;
	when p+q=2n+1. As a consequence, there is a natural bijection between
	genuine irreducible representations of the metaplectic group Mp&lpar;2n,
	R&rpar; and irreducible representations of SO&lpar;p, q&rpar; with
	p+q=2n+1.},
  doi = {10.1023/A:1000450504919},
  eprint = {http://journals.cambridge.org/article_S0010437X98000505},
  file = {:D\:\\eBooks\\papers\\representation\\Jeffrey adams dan barbasch, Genuine representations of the metaplectic group.PDF:PDF},
  url = {http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=308520&fulltextType=RA&fileId=S0010437X98000505}
}

@ARTICLE{Adams19951,
  author = {J. Adams and D. Barbasch},
  title = {Reductive Dual Pair Correspondence for Complex Groups},
  journal = {Journal of Functional Analysis},
  year = {1995},
  volume = {132},
  pages = {1 - 42},
  number = {1},
  doi = {DOI: 10.1006/jfan.1995.1099},
  file = {:D\:\\eBooks\\papers\\representation\\Jeffrey Adams, Dan Barbasch, Reductive Dual Pair Correspondence for Complex Groups.PDF:PDF},
  issn = {0022-1236},
  url = {http://www.sciencedirect.com/science/article/B6WJJ-45NJM69-10/2/1a8be1a3aef709e15a5700a3ce552b1f}
}

@ARTICLE{1992,
  author = {Adams, Jeffrey and Vogan, David A., Jr.},
  title = {L-Groups, Projective Representations, and the Langlands Classification},
  journal = {American Journal of Mathematics},
  year = {1992},
  volume = {114},
  pages = {45--138},
  number = {1},
  copyright = {Copyright 漏 1992 The Johns Hopkins University Press},
  file = {:D\:\\eBooks\\papers\\representation\\Jeffery Adams, David vogan, L-Groups, Projective Representations, and the Langlands Classification.pdf:PDF},
  issn = {00029327},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Feb., 1992},
  publisher = {The Johns Hopkins University Press},
  url = {http://www.jstor.org/stable/2374739}
}

@ARTICLE{Adams1983,
  author = {Adams, J. D.},
  title = {Discrete spectrum of the reductive dual pair (O(p, q), Sp(2m))@ARTICLE{CambridgeJournals:308520,
	
	 author = {ADAMS,JEFFREY and BARBASCH,DAN},
	
	 title = {Genuine Representations of the Metaplectic Group},
	
	 journal = {Compositio Mathematica},
	
	 year = {1998},
	
	 volume = {113},
	
	 pages = {23-66},
	
	 number = {01},
	
	 abstract = { ABSTRACT This paper determines the \&thgr;\&ndash;correspondence
	for
	
	the dual pairs \&lpar;O\&lpar;p, q\&rpar;, Sp\&lpar;2n, R\&rpar;\&rpar;
	
	when p+q=2n+1. As a consequence, there is a natural bijection between
	
	genuine irreducible representations of the metaplectic group Mp\&lpar;2n,
	
	R\&rpar; and irreducible representations of SO\&lpar;p, q\&rpar; with
	
	p+q=2n+1. },
	
	 doi = {10.1023/A:1000450504919},
	
	 eprint = {http://journals.cambridge.org/article_S0010437X98000505},
	
	 url = {http://journals.cambridge.org/action/displayAbstract?fromPage=online\&aid=308520\&fulltextType=RA\&fileId=S0010437X98000505}
	
	}},
  journal = {Inventiones Mathematicae},
  year = {1983},
  volume = {74},
  pages = {449--475},
  number = {3},
  month = oct,
  file = {:D\:\\eBooks\\papers\\representation\\J. D. Adams, Discrete spectrum of the reductive dual pair (O(p, q), Sp(2m)).PDF:PDF},
  owner = {hoxide},
  timestamp = {2009.09.17},
  url = {http://dx.doi.org/10.1007/BF01394246}
}

@ARTICLE{Anh1971,
  author = {Nguyen Huu Anh},
  title = {Restriiction of the principal series of SL (n,C) to some reductive
	subgroups.},
  journal = {Pac. J. Math. },
  year = {1971},
  volume = {38},
  pages = {295-314},
  classmath = {{*22E30 (Analysis on real and complex Lie groups) 43A80 (Analysis
	on other specific Lie groups) 22E45 (Analytic repres.of Lie and linear
	algebraic groups over real fields) }},
  file = {:D\:\\eBooks\\papers\\representation\\Nguyen Huu Anh, Restriction of the principal series of SL(n ,C) to some reductive subgroups.djvu:Djvu},
  keywords = {{group theory}},
  language = {English}
}

@ARTICLE{Asmuth1979,
  author = {Asmuth, Charles},
  title = {Weil Representations of Symplectic p-Adic Groups},
  journal = {American Journal of Mathematics},
  year = {1979},
  volume = {101},
  pages = {885--908},
  number = {4},
  abstract = {Certain Weil representations of Spn(k) are constructed according to
	formulas of M. Saito. Complete decompositions into irreducible summands
	are found. Supercuspidal summands are found and in the case of Sp2(k)
	are shown to be irreducibly induced from compact subgroups. Nonsupercuspidals
	are imbedded in principal series representations in a natural way.},
  copyright = {Copyright © 1979 The Johns Hopkins University Press},
  issn = {00029327},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Aug., 1979},
  publisher = {The Johns Hopkins University Press},
  url = {http://www.jstor.org/stable/2373921}
}

@ARTICLE{Atiyah1973,
  author = {Atiyah, M. and Bott, R. and Patodi, V. K.},
  title = {On the heat equation and the index theorem},
  journal = {Inventiones Mathematicae},
  year = {1973},
  volume = {19},
  pages = {279-330},
  note = {10.1007/BF01425417},
  affiliation = {Mathematical Institute 24-29 St. Giles OX1 3LB Oxford England},
  file = {:D\:\\eBooks\\papers\\representation\\Atiyah, Bottand, Patodi, On the heat equation and the index theorem.PDF:PDF},
  issn = {0020-9910},
  issue = {4},
  keyword = {Mathematics and Statistics},
  publisher = {Springer Berlin / Heidelberg},
  url = {http://dx.doi.org/10.1007/BF01425417}
}

@ARTICLE{BarbaschJan.1999,
  author = {Dan Barbasch and Mladen Bozicevic},
  title = {The Associated Variety of an Induced Representation},
  journal = {Proceedings of the American Mathematical Society},
  year = {Jan., 1999},
  volume = {127},
  pages = {279--288},
  number = {1},
  __markedentry = {[hoxide]},
  abstract = {This paper studies the behavior of the associated variety under induction
	from real parabolic subgroups. We derive a formula for the associated
	variety of an induced module which is analogous to the formula for
	the wave front set of a derived functor module obtained by Barbasch
	and Vogan.},
  file = {:D\:\\eBooks\\papers\\representation\\Dan Barbasch and Mladen Bozicevic, The Associated Variety of an Induced Representation.PDF:PDF},
  issn = {00029939},
  owner = {hoxide},
  publisher = {American Mathematical Society},
  timestamp = {2010.10.26},
  url = {http://www.jstor.org/stable/118942}
}

@ARTICLE{BarbaschVogan1982,
  author = {Barbasch, Dan and Vogan, David},
  title = {Primitive ideals and orbital integrals in complex classical groups},
  journal = {Mathematische Annalen},
  year = {1982},
  volume = {259},
  pages = {153-199},
  note = {10.1007/BF01457308},
  affiliation = {Department of Mathematics Rutgers University 08903 New Brunswick NJ
	USA},
  file = {:D\:\\eBooks\\papers\\representation\\Dan Barbasch, David Vogan, Primitive ideals and orbital integrals in complex classical groups.PDF:PDF},
  issn = {0025-5831},
  issue = {2},
  keyword = {Mathematics and Statistics},
  publisher = {Springer Berlin / Heidelberg},
  url = {http://dx.doi.org/10.1007/BF01457308}
}

@ARTICLE{Barbasch1980,
  author = {Dan Barbasch and David A. Vogan},
  title = {The local structure of characters},
  journal = {Journal of Functional Analysis},
  year = {1980},
  volume = {37},
  pages = {27 - 55},
  number = {1},
  abstract = {Let G be a connected real semisimple Lie group with Lie algebra g.
	Let G = t + s be the Cartan decomposition and K the maximal compact
	subgroup with Lie algebra t. Let [Theta] be the character of an irreducible
	representation. Then [Theta] has an asymptotic expansion at zero
	(in the sense of Taylor series). As consequences of this expansion
	we obtain results about the asymptotic directions in which the K-types
	occur and about the Gelfand-Kirillov dimension of the representation.},
  doi = {DOI: 10.1016/0022-1236(80)90026-9},
  file = {:D\:\\eBooks\\papers\\representation\\Dan Barbasch and David A Vogan,The local structure of characters.PDF:PDF},
  issn = {0022-1236},
  url = {http://www.sciencedirect.com/science/article/B6WJJ-4D8DGTW-43/2/250dc146d32801dd33017a72ddce92f7}
}

@ARTICLE{Bargmann1961,
  author = {Bargmann, V.},
  title = {On a Hilbert space of analytic functions and an associated integral
	transform part I},
  journal = {Communications on Pure and Applied Mathematics},
  year = {1961},
  volume = {14},
  pages = {187--214},
  number = {3},
  file = {:D\:\\eBooks\\papers\\representation\\Bargmann, On a Hilbert space of analytic functions and an associated integral transform part I.pdf:PDF},
  owner = {hoxide},
  timestamp = {2010.04.08},
  url = {http://dx.doi.org/10.1002/cpa.3160140303}
}

@ARTICLE{Bargmann1954,
  author = {Bargmann, V.},
  title = {On Unitary Ray Representations of Continuous Groups},
  journal = {The Annals of Mathematics},
  year = {1954},
  volume = {59},
  pages = {1--46},
  number = {1},
  copyright = {Copyright 1954 Annals of Mathematics},
  file = {:D\:\\eBooks\\papers\\representation\\V. Bargmann, On Unitary Ray Representations of Continuous Groups.PDF:PDF},
  issn = {0003486X},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Jan., 1954},
  publisher = {Annals of Mathematics},
  series = {Second Series},
  url = {http://www.jstor.org/stable/1969831}
}

@BOOK{berline2004heat,
  title = {{Heat kernels and Dirac operators}},
  publisher = {Springer Verlag},
  year = {2004},
  author = {Berline, N. and Getzler, E. and Vergne, M.},
  isbn = {3540200622}
}

@ARTICLE{Bernshtein1971,
  author = {Bernshtein, I. N. and Gel'fand, I. M. and Gel'fand, S. I.},
  title = {Structure of representations generated by vectors of highest weight},
  journal = {Functional Analysis and Its Applications},
  year = {1971},
  volume = {5},
  pages = {1--8},
  number = {1},
  month = jan,
  file = {:D\:\\eBooks\\papers\\representation\\I. N. Bernstein, I.M. Gelfand,S.I. Gelfand, Structure of representations generated by vectors of highest weight.pdf:PDF},
  owner = {hoxide},
  timestamp = {2010.03.12},
  url = {http://dx.doi.org/10.1007/BF01075841}
}

@ARTICLE{BernsteinLunts1996,
  author = {Joseph Bernstein and Valery Lunts},
  title = {A Simple Proof of Kostant's Theorem That $U(\germ{g})$ Is Free over
	Its Center},
  journal = {American Journal of Mathematics},
  year = {1996},
  volume = {118},
  pages = {pp. 979-987},
  number = {5},
  abstract = {In this paper we present a simple proof of the fundamental result
	by B. Kostant which claims that the universal enveloping algebra
	of a reductive Lie algebra $\germ{g}$ is free over its center. We
	also indicate how this result allows to simplify the proof of another
	important result of B. Kostant-the description of the algebra of
	functions on the nilpotent cone. We use this technique to prove some
	generalizations of Kostant's theorem. We also deduce from it a way
	to check which subalgebras of $\germ{g}$ are "centrally free."},
  copyright = {Copyright © 1996 The Johns Hopkins University Press},
  file = {:D\:\\eBooks\\papers\\representation\\Joseph Bernstein, Valery Lunts, A Simple Proof of Kostant's Theorem That U(g) Is Free over Its Center.PDF:PDF},
  issn = {00029327},
  jstor_articletype = {research-article},
  jstor_formatteddate = {Oct., 1996},
  language = {English},
  publisher = {The Johns Hopkins University Press},
  url = {http://www.jstor.org/stable/25098501}
}

@ARTICLE{BinegarZierau1991,
  author = {Binegar, B. and Zierau, R.},
  title = {Unitarization of a singular representation of $SO(p,q)$.},
  journal = {Commun. Math. Phys. },
  year = {1991},
  volume = {138},
  pages = {245-258},
  number = {2},
  abstract = {{From the abstract: ``A geometric construction of a certain singular
	unitary representation of $SO\sb e(p,q)$, with $p+q$ even is given.
	The representation is realized geometrically as the kernel of an
	$SO\sb e(p,q)$-invariant operator on a space of sections over a homogeneous
	space for $SO\sb e(p,q)$. The $K$-structure of these representations
	is elucidated and we demonstrate their unitarity by explicitly writing
	down an ${\germ so}(p,q)$-invariant positive hermitian form. Finally,
	we demonstrate that the annihilator in the universal enveloping algebra
	of this representation is the Joseph ideal, which is the maximal
	primitive ideal associated with the minimal coadjoint orbit''.}},
  classmath = {{*22E70 (Appl. of Lie groups to physics) 22E46 (Semi-simple Lie groups
	and their representations) 81R05 (Repres. of finite-dim. groups and
	algebras from quantum theory) 17B35 (Universal enveloping algebras
	(Lie algebras)) }},
  doi = {10.1007/BF02099491},
  file = {:D\:\\eBooks\\papers\\representation\\B. Binegar and R. Zierau, Unitarization of a singular representation of SO(p,q).pdf:PDF},
  keywords = {{singular unitary representation; homogeneous space; positive hermitian
	form; annihilator; universal enveloping algebra; Joseph ideal; maximal
	primitive ideal; minimal coadjoint orbit}},
  language = {English},
  reviewer = {{P.Holod (Kiev)}}
}

@BOOK{BorelWallach2000,
  title = {Continuous cohomology, discrete subgroups, and representations of
	reductive groups},
  publisher = {American Mathematical Society},
  year = {2000},
  author = {Armand Borel and Nolan Wallach.},
  volume = {67},
  pages = {260},
  series = {Mathematical surveys and monographsMathematical surveys and monographs},
  edition = {2nd},
  owner = {hoxide},
  timestamp = {2009.12.06}
}

@ARTICLE{1994,
  author = {Brylinski, Ranee and Kostant, Bertram},
  title = {Minimal Representations, Geometric Quantization, and Unitarity},
  journal = {Proceedings of the National Academy of Sciences of the United States
	of America},
  year = {1994},
  volume = {91},
  pages = {6026--6029},
  number = {13},
  abstract = {In the framework of geometric quantization we explicitly construct,
	in a uniform fashion, a unitary minimal representation So of every
	simply-connected real Lie group Go such that the maximal compact
	subgroup of Go has finite center and Go admits some minimal representation.
	We obtain algebraic and analytic results about So. We give several
	results on the algebraic and symplectic geometry of the minimal nilpotent
	orbits and then "quantize" these results to obtain the corresponding
	representations. We assume (Lie Go)C is simple.},
  copyright = {Copyright 1994 National Academy of Sciences},
  file = {:D\:\\eBooks\\papers\\representation\\Ranee Brylinski and Bertram kostant, Minimal Representations, Geometric Quantization, and Unitarity.pdf:PDF},
  issn = {00278424},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Jun. 21, 1994},
  publisher = {National Academy of Sciences},
  url = {http://www.jstor.org/stable/2365106}
}

@ARTICLE{BrylinskiKostant1994,
  author = {Ranee Brylinski and Bertram Kostant},
  title = {Nilpotent Orbits, Normality, and Hamiltonian Group Actions},
  journal = {Journal of the American Mathematical Society},
  year = {1994},
  volume = {7},
  pages = {269--298},
  number = {2},
  copyright = {Copyright 漏 1994 American Mathematical Society},
  file = {:D\:\\eBooks\\papers\\representation\\Ranee Brylinski and Bertram Kostant, Nilpotent Orbits, Normality, and Hamiltonian Group Actions.pdf:PDF},
  issn = {08940347},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Apr., 1994},
  publisher = {American Mathematical Society},
  url = {http://www.jstor.org/stable/2152759}
}

@INPROCEEDINGS{Cartier1966,
  author = {Pierre Cartier},
  title = {Quantum Mechanical Commutation Relations and Theta Functions},
  booktitle = {Proceedings of Symposia in Pure Mathematics},
  year = {1966},
  editor = {Armand Borel and George D. Mostow},
  volume = {9},
  publisher = {American Mathematical Society},
  file = {:D\:\\eBooks\\papers\\representation\\Proceedings of Symposia in Pure Math 9, IV.pdf:PDF},
  owner = {hoxide},
  timestamp = {2009.11.07}
}

@ARTICLE{Dadok1985,
  author = {Jiri Dadok},
  title = {Polar Coordinates Induced by Actions of Compact Lie Groups},
  journal = {Transactions of the American Mathematical Society},
  year = {1985},
  volume = {288},
  pages = {pp. 125-137},
  number = {1},
  abstract = {Let G be a connected Lie subgroup of the real orthogonal group O(n).
	For the action of G on Rn, we construct linear subspaces a that intersect
	all orbits. We determine for which G there exists such an a meeting
	all the G-orbits orthogonally; groups that act transitively on spheres
	are obvious examples. With few exceptions all possible G arise as
	the isotropy subgroups of Riemannian symmetric spaces.},
  copyright = {Copyright © 1985 American Mathematical Society},
  file = {:D\:\\eBooks\\papers\\representation\\Jiri Dadok, Polar Coordinates Induced by Actions of Compact Lie Groups.PDF:PDF},
  issn = {00029947},
  jstor_articletype = {research-article},
  jstor_formatteddate = {Mar., 1985},
  language = {English},
  publisher = {American Mathematical Society},
  url = {http://www.jstor.org/stable/2000430}
}

@ARTICLE{Daszkiewicz2005,
  author = {Daszkiewicz, Andrzej and Kra\'skiewicz, Witold and Przebinda, Tomasz},
  title = {Dual pairs and Kostant-Sekiguchi correspondence. II. Classification
	of nilpotent elements},
  journal = {Central European Journal of Mathematics},
  year = {2005},
  volume = {3},
  pages = {430-474},
  note = {10.2478/BF02475917},
  abstract = {We classify the homogeneous nilpotent orbits in certain Lie color
	algebras and specialize the results to the setting of a real reductive
	dual pair. For any member of a dual pair, we prove the bijectivity
	of the two Kostant-Sekiguchi maps by straightforward argument. For
	a dual pair we determine the correspondence of the real orbits, the
	correspondence of the complex orbits and explain how these two relations
	behave under the Kostant-Sekiguchi maps. In particular we prove that
	for a dual pair in the stable range there is a Kostant-Sekiguchi
	map such that the conjecture formulated in [6] holds. We also show
	that the conjecture cannot be true in general.},
  affiliation = {Nicholas Copernicus University Faculty of Mathematics Chopina 12 87-100
	Toruń Poland},
  file = {:D\:\\eBooks\\papers\\representation\\Daszkiewicz,Kraskiewicz, Przebinda, Dual pairs and Kostant-Sekiguchi correspondence. II. Classification of nilpotent elements.PDF:PDF},
  issn = {1895-1074},
  issue = {3},
  keyword = {Mathematics and Statistics},
  publisher = {Versita, co-published with Springer-Verlag GmbH},
  url = {http://dx.doi.org/10.2478/BF02475917}
}

@ARTICLE{Daszkiewicz1997518,
  author = {Andrzej Daszkiewicz and Witold Kraskiewicz and Tomasz Przebinda},
  title = {Nilpotent Orbits and Complex Dual Pairs},
  journal = {Journal of Algebra},
  year = {1997},
  volume = {190},
  pages = {518 - 539},
  number = {2},
  doi = {DOI: 10.1006/jabr.1996.6910},
  file = {:D\:\\eBooks\\papers\\representation\\Andrzej Daszkiewicz and Witold Kraskiewicz and Tomasz Przebinda, Nilpotent Orbits and Complex Dual Pairs.PDF:PDF},
  issn = {0021-8693},
  url = {http://www.sciencedirect.com/science/article/B6WH2-45PTYN8-1X/2/07e1f93c772a4b168acfceee80c25d60}
}

@ARTICLE{1991,
  author = {Debarre, Olivier and Ton-That, Tuong},
  title = {Representations of SO(k, C) on Harmonic Polynomials on a Null Cone},
  journal = {Proceedings of the American Mathematical Society},
  year = {1991},
  volume = {112},
  pages = {31--44},
  number = {1},
  abstract = {The linear action of the group SO(k, C) on the vector space Cn 脳 k
	extends to an action on the algebra of polynomials on Cn 脳 k. The
	polynomials that are fixed under this action are called SO(k, C)-invariant.
	The SO(k, C)-harmonic polynomials are common solutions of the SO(k,
	C)-invariant differential operators. The ideal of all SO(k, C)-invariants
	without constant terms, the null cone of this ideal, and the orbits
	of SO(k, C) on this null cone are studied in great detail. All irreducible
	holomorphic representations of SO(k, C) are concretely realized on
	the space of SO(k, C)-harmonic polynomials.},
  copyright = {Copyright 1991 American Mathematical Society},
  file = {:D\:\\eBooks\\papers\\representation\\Olivier Debarre, Tuong Ton-That, Representations of SO(k, C) on Harmonic Polynomials on a Null Cone.PDF:PDF},
  issn = {00029939},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {May, 1991},
  publisher = {American Mathematical Society},
  url = {http://www.jstor.org/stable/2048477}
}

@BOOK{Dixmier1982,
  title = {$C^*$-algebras},
  publisher = {North-Holland},
  year = {1982},
  author = {Jacques Dixmier}
}

@ARTICLE{Donkin1988,
  author = {Donkin, S.},
  title = {On conjugating representations and adjoint representations of semisimple
	groups},
  journal = {Inventiones Mathematicae},
  year = {1988},
  volume = {91},
  pages = {137-145},
  note = {10.1007/BF01404916},
  affiliation = {School of Mathematical Sciences Queen Mary College Mile End Rd. E1
	4NS London England, UK},
  file = {:D\:\\eBooks\\papers\\representation\\S. Donkin,On conjugating  representations and adjoint  representations.PDF:PDF},
  issn = {0020-9910},
  issue = {1},
  keyword = {Mathematics and Statistics},
  owner = {hoxide},
  publisher = {Springer Berlin / Heidelberg},
  timestamp = {2010.08.23},
  url = {http://dx.doi.org/10.1007/BF01404916}
}

@ARTICLE{Duflo1970,
  author = {Duflo, M.},
  title = {Fundamental-series representations of a semisimple Lie group},
  journal = {Functional Analysis and Its Applications},
  year = {1970},
  volume = {4},
  pages = {122--126},
  number = {2},
  month = apr,
  file = {:D\:\\eBooks\\papers\\representation\\Duflo,Fundamental-series representations of a semisimple Lie group.pdf:PDF},
  owner = {hoxide},
  timestamp = {2010.05.01},
  url = {http://dx.doi.org/10.1007/BF01094488}
}

@ARTICLE{Dvorsky1999,
  author = {Dvorsky, Alexander and Sahi, Siddhartha},
  title = {Explicit Hilbert spaces for certain unipotent representations II},
  journal = {Inventiones Mathematicae},
  year = {1999},
  volume = {138},
  pages = {203--224},
  number = {1},
  month = oct,
  file = {:D\:\\eBooks\\papers\\representation\\Alexander Dvorsky, Siddhartha Sahi, Explicit Hilbert spaces for certain unipotent representations II.pdf:PDF},
  owner = {hoxide},
  timestamp = {2010.07.11},
  url = {http://dx.doi.org/10.1007/s002220050347}
}

@CONFERENCE{Enright1983,
  author = {Thomas Enright and Roger Howe and Nolan Wallach},
  title = {A classification of unitary highest weight modules},
  booktitle = {Representation theory of reductive groups},
  year = {1983},
  volume = {40},
  series = {Progr. Math.},
  publisher = {Birkh\"{a}user Boston},
  file = {:D\:\\eBooks\\papers\\representation\\Thomas Enright, Roger Howe,  Nolan Wallach, A classification of unitary highest weight modules.pdf:PDF},
  owner = {hoxide},
  timestamp = {2009.10.08}
}

@ARTICLE{Enright1985,
  author = {Enright, T. and Parthasarathy, R. and Wallach, N. and Wolf, J.},
  title = {Unitary derived functor modules with small spectrum},
  journal = {Acta Mathematica},
  year = {1985},
  volume = {154},
  pages = {105--136},
  number = {1},
  month = mar,
  file = {:D\:\\eBooks\\papers\\representation\\T.J.Enright, R.Parthasarathy, N.R. wallach, J.A. Wolf, Unitary derived functor modules with small spectrum.pdf:PDF},
  owner = {hoxide},
  timestamp = {2010.06.10},
  url = {http://dx.doi.org/10.1007/BF02392820}
}

@ARTICLE{EnrightWallach1980,
  author = {Enright, T.J. and Wallach, N.R.},
  title = {Notes on homological algebra and representations of Lie algebras.},
  journal = {Duke Math. J. },
  year = {1980},
  volume = {47},
  pages = {1-15},
  classmath = {{*17B55 (Homological methods in theory of Lie algebras) 22E45 (Analytic
	repres.of Lie and linear algebraic groups over real fields) }},
  doi = {10.1215/S0012-7094-80-04701-8},
  file = {:D\:\\eBooks\\papers\\representation\\Enright wallach, Notes on Homological algebra and representations of Lie Algebras.pdf:PDF},
  keywords = {{discrete series representations; irreducible representations; Bott-Borel-
	Weil theorem}},
  language = {English}
}

@ARTICLE{Enright1978,
  author = {Enright, Thomas and Wallach, Nolan},
  title = {The fundamental series of representations of a real semisimple Lie
	algebra},
  journal = {Acta Mathematica},
  year = {1978},
  volume = {140},
  pages = {1--32},
  number = {1},
  month = dec,
  abstract = {Without Abstract},
  file = {:D\:\\eBooks\\papers\\representation\\Thomas J. Enright, Nolan R. Wallach, The fundamental series of representations of a real semisimple Lie algebra.PDF:PDF},
  owner = {hoxide},
  timestamp = {2009.05.18},
  url = {http://dx.doi.org/10.1007/BF02392301}
}

@ARTICLE{Enright1975,
  author = {Enright, Thomas J. and Varadarajan, V. S.},
  title = {On an Infinitesimal Characterization of the Discrete Series},
  journal = {The Annals of Mathematics},
  year = {1975},
  volume = {102},
  pages = {1--15},
  number = {1},
  copyright = {Copyright 1975 Annals of Mathematics},
  file = {:D\:\\eBooks\\math\\papers\\representations\\Thomas J. Enright\\On an Infinitesimal Characterization of the Discrete Series.PDF:PDF},
  issn = {0003486X},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Jul., 1975},
  publisher = {Annals of Mathematics},
  series = {Second Series},
  url = {http://www.jstor.org/stable/1970970}
}

@ARTICLE{Enright1997,
  author = {Enright, Thomas J. and Wallach, Nolan R.},
  title = {Embeddings of unitary highest weight representations and generalized
	Dirac operators},
  journal = {Mathematische Annalen},
  year = {1997},
  volume = {307},
  pages = {627--646},
  number = {4},
  month = apr,
  file = {:D\:\\eBooks\\papers\\representation\\Thomas J. Enright and Nolan R.Wallach,Embeddings of unitary highest weight representations and generalized Dirac operators.pdf:PDF},
  owner = {hoxide},
  timestamp = {2010.04.24},
  url = {http://dx.doi.org/10.1007/s002080050053}
}

@ARTICLE{1980,
  author = {Flensted-Jensen, Mogens},
  title = {Discrete Series for Semisimple Symmetric Spaces},
  journal = {The Annals of Mathematics},
  year = {1980},
  volume = {111},
  pages = {253--311},
  number = {2},
  abstract = {We give a sufficient condition for the existence of minimal closed
	G-invariant subspaces of L2(G / H) for a semisimple symmetric space
	G / H. As a semisimple Lie group with finite center may always be
	considered as a symmetric space, thisprovides, in particular, a new
	and elementary proof of Harish-Chandra's result that G has a discrete
	series if rand (G) = rank K, where K is a maximal compact subgroup.},
  copyright = {Copyright 1980 Annals of Mathematics},
  file = {:D\:\\eBooks\\papers\\representation\\Mogens Flensted-Jensen, Discrete Series for Semisimple Symmetric Spaces.PDF:PDF},
  issn = {0003486X},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Mar., 1980},
  publisher = {Annals of Mathematics},
  series = {Second Series},
  url = {http://www.jstor.org/stable/1971201}
}

@ARTICLE{FlenstedJensen1978,
  author = {Mogens Flensted-Jensen},
  title = {Spherical functions on a real semisimple Lie group. A method of reduction
	to the complex case},
  journal = {Journal of Functional Analysis},
  year = {1978},
  volume = {30},
  pages = {106 - 146},
  number = {1},
  abstract = {The spherical functions on a real semisimple Lie group (w.r.t. a maximal
	compact subgroup) are characterized as joint eigenfunctions of certain
	differential operators on the corresponding complex group. Using
	this, several results concerning the spherical Fourier transform
	on the real group are reduced to the corresponding results for the
	complex group. When the group in question is a normal real form,
	this leads to new and simpler proofs of such results as the Plancherel
	formula, the Paley-Wiener theorem and the characterization of the
	image under the spherical Fourier transform of the L1- and L2-Schwartz
	spaces. In these proofs neither any knowledge of Harish-Chandras
	c-function nor the series expansion for the spherical function are
	used. For the proof of the main result some analysis of independent
	interest on pseudo-Riemannian symmetric spaces is developed. Such
	as a generalized Cartan decomposition and a method of analytic continuation
	between two #dual# pseudo-Riemannian symmetric spaces.},
  doi = {DOI: 10.1016/0022-1236(78)90058-7},
  file = {:D\:\\eBooks\\papers\\representation\\Mogens Flensted-Jensen, Spherical functions on a real semisimple Lie group. A method of reduction to the complex case.PDF:PDF},
  issn = {0022-1236},
  url = {http://www.sciencedirect.com/science/article/B6WJJ-4CRJ1MD-S2/2/b39df3c2ceb8a56e6235be3f1ef952db}
}

@ARTICLE{Frajria1991,
  author = {Frajria, Pierluigi M\"oseneder},
  title = {Derived Functors of Unitary Highest Weight Modules at Reduction Points},
  journal = {Transactions of the American Mathematical Society},
  year = {1991},
  volume = {327},
  pages = {703--738},
  number = {2},
  abstract = {The derived functors introduced by Zuckerman are applied to the unitary
	highest weight modules of the Hermitian symmetric pairs of classical
	type. The construction yields "small" unitary representations which
	do not have a highest weight. The infinitesimal character parameter
	of the modules we consider is such that their derived functors are
	nontrivial in more than one degree; at the extreme degrees where
	the cohomology is nonvanishing, it is possible to determine the K-spectrum
	of the resulting representations completely. Using this information
	it is shown that, in most cases, the derived functor modules are
	unitary, irreducible, and not of highest weight type. Their infinitesimal
	character and lowest K-type are also easily computed.},
  copyright = {Copyright 1991 American Mathematical Society},
  file = {:D\:\\eBooks\\papers\\representation\\Pierluigi Moseneder Frajria, Derived Functors of Unitary Highest Weight Modules at Reduction Points.pdf:PDF},
  issn = {00029947},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Oct., 1991},
  publisher = {American Mathematical Society},
  url = {http://www.jstor.org/stable/2001820}
}

@BOOK{Fulton1991,
  title = {Representation theory: A first course},
  publisher = {Springer},
  year = {1991},
  author = {Fulton, W. and Harris, J.},
  number = {129},
  series = {graduate texts in mathematics}
}

@ARTICLE{GanSavin2005,
  author = {Wee Teck Gan and Gordan Savin},
  title = {On minimal representations definitions and properties},
  journal = {Represent. Theory},
  year = {2005},
  volume = {9},
  pages = {46-93},
  doi = {10.1090/S1088-4165-05-00191-3},
  file = {:D\:\\eBooks\\papers\\representation\\Wee Teck Gan, Gordan Savin, On minimal representations definitions and properties.PDF:PDF},
  owner = {hoxide},
  timestamp = {2010.10.29}
}

@ARTICLE{Garland1976,
  author = {Garland, Howard and Lepowsky, James},
  title = {Lie algebra homology and the Macdonald-Kac formulas},
  journal = {Inventiones Mathematicae},
  year = {1976},
  volume = {34},
  pages = {37--76},
  number = {1},
  month = feb,
  file = {:D\:\\eBooks\\papers\\representation\\H. Garland, J. Lepowsky, Lie algebra homology and the Macdonald-Kac formulas.pdf:PDF},
  owner = {hoxide},
  timestamp = {2009.09.30},
  url = {http://dx.doi.org/10.1007/BF01418970}
}

@ARTICLE{Gauger1976,
  author = {Gauger, Michael A.},
  title = {Some remarks on the center of the universal enveloping algebra of
	a classical simple Lie algebra},
  journal = {Pacific Journal of Mathematics},
  year = {1976},
  volume = {62},
  pages = {93-97},
  classmath = {{*17B35 (Universal enveloping algebras (Lie algebras))}},
  file = {:D\:\\eBooks\\papers\\representation\\Michael A. Gauger, Some remarks on the center of the universal enveloping algebra of a classical simple Lie algebra.pdf:PDF},
  language = {English}
}

@INPROCEEDINGS{Gelbart1979,
  author = {Stephen Gelbart},
  title = {Examples of dual reductive pairs},
  booktitle = {Proceedings of Symposia in Pure Mathematics},
  year = {1979},
  volume = {33},
  pages = {287-296},
  publisher = {AMS},
  file = {:D\:\\eBooks\\papers\\representation\\Stephen Gelbart, Examples of dual reductive pairs.pdf:PDF},
  owner = {hoxide},
  timestamp = {2010.04.08}
}

@ARTICLE{Gross1977,
  author = {Kenneth I. Gross and Ray A. Kunze},
  title = {Bessel functions and representation theory, II holomorphic discrete
	series and metaplectic representations},
  journal = {Journal of Functional Analysis},
  year = {1977},
  volume = {25},
  pages = {1 - 49},
  number = {1},
  doi = {DOI: 10.1016/0022-1236(77)90030-1},
  file = {:D\:\\eBooks\\papers\\representation\\Gross, Kunze, Bessel functions and representation theory, II holomorphic discrete series and metaplectic representations.PDF:PDF},
  issn = {0022-1236},
  url = {http://www.sciencedirect.com/science/article/B6WJJ-4D8DH3D-5P/2/5f280341f6f385ab80b637f169b4e41a}
}

@ARTICLE{1957,
  author = {Harish-Chandra},
  title = {Fourier Transforms on a Semisimple Lie Algebra I},
  journal = {American Journal of Mathematics},
  year = {1957},
  volume = {79},
  pages = {pp. 193-257},
  number = {2},
  copyright = {Copyright © 1957 The Johns Hopkins University Press},
  file = {:D\:\\eBooks\\papers\\representation\\harish Chandra, Fourier Transforms on a Semisimple Lie Algebra I.PDF:PDF},
  issn = {00029327},
  jstor_articletype = {research-article},
  jstor_formatteddate = {Apr., 1957},
  language = {English},
  publisher = {The Johns Hopkins University Press},
  url = {http://www.jstor.org/stable/2372680}
}

@ARTICLE{1956,
  author = {Harish-Chandra},
  title = {Representations of Semisimple Lie Groups, V},
  journal = {American Journal of Mathematics},
  year = {1956},
  volume = {78},
  pages = {1--41},
  number = {1},
  copyright = {Copyright 1956 The Johns Hopkins University Press},
  file = {:D\:\\eBooks\\papers\\representation\\Harish Chandra, Representations of semisimple lie groups V.PDF:PDF},
  issn = {00029327},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Jan., 1956},
  publisher = {The Johns Hopkins University Press},
  url = {http://www.jstor.org/stable/2372481}
}

@ARTICLE{1955,
  author = {Harish-Chandra},
  title = {Representations of Semisimple Lie Groups IV},
  journal = {American Journal of Mathematics},
  year = {1955},
  volume = {77},
  pages = {743--777},
  number = {4},
  copyright = {Copyright 1955 The Johns Hopkins University Press},
  file = {:D\:\\eBooks\\papers\\representation\\Harish Chandra, Representations of semisimple lie groups IV.PDF:PDF},
  issn = {00029327},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Oct., 1955},
  publisher = {The Johns Hopkins University Press},
  url = {http://www.jstor.org/stable/2372596}
}

@ARTICLE{HarishChandra1949,
  author = {Harish-Chandra},
  title = {On Representations of Lie Algebras},
  journal = {The Annals of Mathematics},
  year = {1949},
  volume = {50},
  pages = {900--915},
  number = {4},
  copyright = {Copyright 1949 Annals of Mathematics},
  file = {:D\:\\eBooks\\papers\\representation\\harish Chandra, On representations of lie algebras.pdf:PDF},
  issn = {0003486X},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Oct., 1949},
  publisher = {Annals of Mathematics},
  series = {Second Series},
  url = {http://www.jstor.org/stable/1969586}
}

@ARTICLE{Helgason1992,
  author = {Helgason, Sigurdur},
  title = {Some Results on Invariant Differential Operators on Symmetric Spaces},
  journal = {American Journal of Mathematics},
  year = {1992},
  volume = {114},
  pages = {789--811},
  number = {4},
  copyright = {Copyright 1992 The Johns Hopkins University Press},
  file = {:D\:\\eBooks\\math\\papers\\representations\\Sigurdur Helgason\\Some Results on Invariant Differential Operators on Symmetric Spaces.PDF:PDF},
  issn = {00029327},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Aug., 1992},
  publisher = {The Johns Hopkins University Press},
  url = {http://www.jstor.org/stable/2374798}
}

@ARTICLE{Hochschild1956,
  author = {Hochschild, G.},
  title = {Relative Homological Algebra},
  journal = {Transactions of the American Mathematical Society},
  year = {1956},
  volume = {82},
  pages = {246--269},
  number = {1},
  copyright = {Copyright 1956 American Mathematical Society},
  file = {:D\:\\eBooks\\papers\\representation\\Hochschild, Relative Homological Algebra.PDF:PDF},
  issn = {00029947},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {May, 1956},
  publisher = {American Mathematical Society},
  url = {http://www.jstor.org/stable/1992988}
}

@INPROCEEDINGS{Howe1979,
  author = {Roger Howe},
  title = {theta-series and invariant theory},
  booktitle = {Automorphic Forms, Representations, and L-Functions, Part 1},
  year = {1979},
  editor = {A. Borel, W. Casselman},
  volume = {33},
  pages = {1979},
  publisher = {AMS},
  file = {:D\:\\eBooks\\papers\\representation\\Roger Howe, theta-series and invariant theory.PDF:PDF},
  owner = {hoxide},
  timestamp = {2009.08.15}
}

@INCOLLECTION{Howe1985,
  author = {Roger Howe},
  title = {Dual pairs in physics: Harmonic oscillators, photons, electrons and
	singletons},
  booktitle = {Applications of Group Theory in Physics and Mathematical Physics},
  publisher = {American Mathematical Society},
  year = {1985},
  editor = {Moshe Flato and Paul Sally and Gregg Zuckerman},
  volume = {21},
  series = {Lectures in Applied Mathematics},
  pages = {179-206},
  owner = {hoxide},
  timestamp = {2009.11.18}
}

@ARTICLE{HoweOsc1,
  author = {Roger Howe},
  title = {Oscillator representation, algebraic setup},
  journal = {perprint},
  owner = {hoxide},
  timestamp = {2010.09.08}
}

@ARTICLE{HoweOsc2,
  author = {Roger Howe},
  title = {Oscillator representation, analytic setup},
  journal = {perprint},
  owner = {hoxide},
  timestamp = {2010.09.08}
}

@CONFERENCE{Howe1995perspective,
  author = {Roger Howe},
  title = {Perspective in invariant theory: Schur duality, multiplicity free
	actions and beyond, The Schur Lecture (Tel Aviv 1992)},
  booktitle = {srael mathematical conference proceedings},
  year = {1995},
  volume = {8},
  pages = {236},
  publisher = {American Mathematical Society}
}

@ARTICLE{Howe1989Rem,
  author = {Howe, Roger},
  title = {Remarks on Classical Invariant Theory},
  journal = {Transactions of the American Mathematical Society},
  year = {1989},
  volume = {313},
  pages = {539--570},
  number = {2},
  abstract = {A uniform formulation, applying to all classical groups simultaneously,
	of the First Fundamental Theory of Classical Invariant Theory is
	given in terms of the Weyl algebra. The formulation also allows skew-symmetric
	as well as symmetric variables. Examples illustrate the scope of
	this formulation.},
  copyright = {Copyright 1989 American Mathematical Society},
  file = {:D\:\\eBooks\\papers\\representation\\Roger Howe, Remarks on Classical Invariant Theory.PDF:PDF},
  issn = {00029947},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Jun., 1989},
  publisher = {American Mathematical Society},
  url = {http://www.jstor.org/stable/2001418}
}

@ARTICLE{Howe1989Tran,
  author = {Howe, Roger},
  title = {Transcending Classical Invariant Theory},
  journal = {Journal of the American Mathematical Society},
  year = {1989},
  volume = {2},
  pages = {535--552},
  number = {3},
  copyright = {Copyright 1989 American Mathematical Society},
  file = {:D\:\\eBooks\\papers\\representation\\Roger Howe, Transcending Classical Invariant Theory.PDF:PDF},
  issn = {08940347},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Jul., 1989},
  publisher = {American Mathematical Society},
  url = {http://www.jstor.org/stable/1990942}
}

@ARTICLE{Howe1980,
  author = {Roger Howe},
  title = {On the role of the Heisenberg group in harmonic analysis},
  journal = {Bull. Amer. Math. Soc., New Ser.},
  year = {1980},
  volume = {3},
  pages = {821-843},
  classmath = {{*43-02 (Research monographs (abstract harmonic analysis)) 43A45 (Spectral
	synthesis on groups, etc.) 58J40 (Pseudodifferential and Fourier
	integral operators on manifolds) 35-02 (Research monographs (partial
	differential equations)) 22-02 (Research monographs (topological
	groups)) }},
  doi = {10.1090/S0273-0979-1980-14825-9},
  file = {:D\:\\eBooks\\papers\\representation\\Roger Howe, On the role of the Heisenberg group in harmonic analysis.PDF:PDF},
  keywords = {{Heisenberg group; Fourier transform; Bochner's formula; (Sl2, Opq)
	duality; symbols; pseudo-differential operators}},
  language = {English}
}

@INCOLLECTION{howe1980notion,
  author = {Howe, R.},
  title = {On a notion of rank for unitary representations of the classical
	groups},
  year = {1980},
  pages = {223--331},
  journal = {Harmonic analysis and group representations}
}

@ARTICLE{Howe1980Quantum,
  author = {Roger Howe},
  title = {Quantum mechanics and partial differential equations},
  journal = {Journal of Functional Analysis},
  year = {1980},
  volume = {38},
  pages = {188 - 254},
  number = {2},
  abstract = {This paper develops the basic theory of pseudo-differential operators
	on Rn, through the Calder-Vaillancourt (0, 0) L2-estimate, as a natural
	part of the harmonic analysis on the Heisenberg group, the group-theoretic
	embodiment of Heisenberg's Canonical Commutation Relations. The symbol
	mapping is given a group-theoretic interpretation consistent with
	the Kirillov method of orbits. By comparing different well-known
	realizations of the unique irreducible representation of the Heisenberg
	group, the Toeplitz operators on the complex n-ball are shown essentially
	to be pseudo-differential operators. The proof of the Calder-Vaillancourt
	estimate is almost purely group-theoretic. Criteria for positivity,
	and for compactness are also given.},
  doi = {DOI: 10.1016/0022-1236(80)90064-6},
  file = {:D\:\\eBooks\\papers\\representation\\roger howe, Quantum mechanics and partial differential equations.PDF:PDF},
  issn = {0022-1236},
  url = {http://www.sciencedirect.com/science/article/B6WJJ-4CRJ1C5-P1/2/8af6a10cd9d111549b2485250c74303f}
}

@ARTICLE{HoweLee2006a,
  author = {Roger Howe and Soo Teck Lee},
  title = {Bases for some reciprocity algebras I},
  journal = {Trans. Amer. Math. Soc. },
  year = {2007},
  volume = {359},
  pages = {4359-4387},
  doi = {10.1090/S0002-9947-07-04142-6},
  file = {:D\:\\eBooks\\papers\\representation\\Roger Howe, Soo Teck Lee, Bases for some reciprocity algebras I.pdf:PDF},
  owner = {hoxide},
  timestamp = {2010.05.08}
}

@ARTICLE{CambridgeJournals:554408,
  author = {Howe,Roger and Lee,Soo Teck},
  title = {Bases for some reciprocity algebras III},
  journal = {Compositio Mathematica},
  year = {2006},
  volume = {142},
  pages = {1594-1614},
  number = {06},
  abstract = { ABSTRACT We construct bases for the stable branching algebras for
	the symmetric pairs $(\mathrm{GL}_{2n},\mathrm{Sp}_{2n}),\ (\mathrm{Sp}_{2(n+m)},
	\mathrm{Sp}_{2n}\times\mathrm{Sp}_{2m})$ and $(\mathrm{O}_{2n},\mathrm{GL}_{n})$.
	Each basis element is expressed as a sum of products of pfaffians.
	},
  doi = {10.1112/S0010437X06002399},
  eprint = {http://journals.cambridge.org/article_S0010437X06002399},
  file = {:D\:\\eBooks\\papers\\representation\\Roger Howe, Soo Teck Lee, Bases for some reciprocity algebras III.pdf:PDF},
  url = {http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=554408&fulltextType=RA&fileId=S0010437X06002399}
}

@ARTICLE{HoweLee2006b,
  author = {Roger Howe and Soo Teck Lee},
  title = {Bases for some reciprocity algebras II},
  journal = {Advances in Mathematics},
  year = {2006},
  volume = {206},
  pages = {145 - 210},
  number = {1},
  abstract = {We construct bases for the stable branching algebras for the symmetric
	pairs (GLn,On), (On+m,On+m) and (Sp2n,GLn).},
  doi = {DOI: 10.1016/j.aim.2005.08.006},
  file = {:D\:\\eBooks\\papers\\representation\\Roger Howe, Soo Teck Lee, Bases for some reciprocity algebras II.pdf:PDF},
  issn = {0001-8708},
  keywords = {Reciprocity algebra},
  url = {http://www.sciencedirect.com/science/article/B6W9F-4H57JT4-2/2/876893c95c95a8be8de31ed1f845c972}
}

@ARTICLE{Howe2002eigendistributions,
  author = {Roger Howe and Chen-Bo Zhu},
  title = {Eigendistributions for orthogonal groups and representations of symplectic
	groups},
  journal = {Journal f{\\"u}r die reine und angewandte Mathematik (Crelles Journal)},
  year = {2002},
  volume = {2002},
  pages = {121--166},
  number = {545},
  file = {:D\:\\eBooks\\papers\\representation\\Roger Howe, Chen-Bo Zhu, Eigendistributions for orthogonal groups and representations of symplectic groups.PDF:PDF},
  publisher = {Walter de Gruyter GmbH \& Co. KG Berlin, Germany}
}

@ARTICLE{0794.22012,
  author = {Howe, Roger E. and Tan, Eng-Chye},
  title = {Homogeneous functions on light cones: The infinitesimal structure
	of some degenerate principal series representations.},
  journal = {Bull. Am. Math. Soc., New Ser. },
  year = {1993},
  volume = {28},
  pages = {1-74},
  number = {1},
  abstract = {The authors analyze in a systematic fashion the structure of some
	degenerate principal series representations of real classical simple
	Lie groups $\text{O}(p,q)$, $\text{U}(p,q)$ and $\text{Sp}(p,q)$.
	Their elementary method can be viewed as a refinement of the classical
	arguments of V. Bargmann used in the classification of irreducible
	admissible representations of $\text{SL}(2,\bbfR)$.},
  classmath = {{*22E46 (Semi-simple Lie groups and their representations) 17B10 (Representations
	of Lie algebras, algebraic theory) }},
  doi = {10.1090/S0273-0979-1993-00360-4},
  file = {:D\:\\eBooks\\papers\\representation\\Howe, Roger E., Tan, Eng-Chye Homogeneous functions on light cones the infinitesimal structure of some degenerate principal series representations.PDF:PDF},
  keywords = {{degenerate principal series representations; simple Lie groups; irreducible
	admissible representations}},
  language = {English},
  reviewer = {{D.Mili\v{c}i\'c (Salt Lake City)}}
}

@ARTICLE{HuangJun.1999,
  author = {Huang, Jing-Song and Li, Jian-Shu},
  title = {Unipotent Representations Attached to Spherical Nilpotent Orbits},
  journal = {American Journal of Mathematics},
  year = {Jun., 1999},
  volume = {121},
  pages = {497--517},
  number = {3},
  abstract = {A coadjoint nilpotent orbit ${\cal O}$ of a complex semisimple Lie
	group G is said to be spherical if it contains an open orbit of a
	Borel subgroup. We determine when and how to attach unitary representations
	to such an orbit for the real orthogonal and symplectic groups. Our
	results actually extend to a larger class of nilpotent coadjoint
	orbits.},
  file = {:D\:\\eBooks\\papers\\representation\\Huang Jing Song, Li Jian Shu, Unipotent Representations Attached to Spherical Nilpotent Orbits.PDF:PDF},
  issn = {00029327},
  owner = {hoxide},
  publisher = {The Johns Hopkins University Press},
  timestamp = {2010.10.20},
  url = {http://www.jstor.org/stable/25098935}
}

@ARTICLE{HuangZhu1999,
  author = {Huang, Jing-Song and Zhu, Chen-Bo},
  title = {Weyl's Construction and Tensor Power Decomposition for G2},
  journal = {Proceedings of the American Mathematical Society},
  year = {1999},
  volume = {127},
  pages = {925--934},
  number = {3},
  abstract = {Let V be the 7-dimensional irreducible representations of G2. We decompose
	the tensor power V^n into irreducible representations of G2 and obtain
	all irreducible representations of G2 in the decomposition. This
	generalizes Weyl's work on the construction of irreducible representations
	and decomposition of tensor products for classical groups to the
	exceptional group G2.},
  copyright = {Copyright 1999 American Mathematical Society},
  file = {:D\:\\eBooks\\papers\\representation\\Huang JingSong, Zhu Chenbo, Weyl's Construction and Tensor Power Decomposition for G2.pdf:PDF},
  issn = {00029939},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Mar., 1999},
  publisher = {American Mathematical Society},
  url = {http://www.jstor.org/stable/119028}
}

@BOOK{Humphreys1972,
  title = {Introduction to Lie algebras and representation theory},
  publisher = {Springer-Verlag},
  year = {1972},
  author = {Humphreys, James E},
  owner = {hoxide},
  timestamp = {2010.05.09}
}

@ARTICLE{Jackson20092607,
  author = {Steven Glenn Jackson and Alfred G. Noel},
  title = {A new approach to computing generators for $U(\mathfrak{g})^K$},
  journal = {Journal of Algebra},
  year = {2009},
  volume = {322},
  pages = {2607 - 2620},
  number = {8},
  abstract = {Let (G,K) be the complex symmetric pair associated with a real reductive
	Lie group G0. We discuss an algorithmic approach to computing generators
	for the centralizer of K in the universal enveloping algebra of .
	In particular, we compute explicit generators for the cases G0=SU(2,2),
	, , , and the exceptional group G2(2).},
  doi = {DOI: 10.1016/j.jalgebra.2009.07.004},
  file = {:D\:\\eBooks\\papers\\representation\\Steven Glenn Jackson and Alfred G Noel, A new approach to computing generators for U(g)K.pdf:PDF},
  issn = {0021-8693},
  keywords = {Semisimple Lie group},
  url = {http://www.sciencedirect.com/science/article/B6WH2-4WXXV99-1/2/8c222004bc478c5cf385c6c802d9401b}
}

@BOOK{Jacobson1953,
  title = {{Lectures in abstract algebra, Vol. II, Linear Algebra}},
  publisher = {D. Van Nostrand Company},
  year = {1953},
  author = {Nathan Jacobson},
  volume = {2},
  number = {9904},
  pages = {11628--8},
  journal = {Bull. Amer. Math. Soc. 73 (1967), 44-46. DOI: 10.1090/S0002-9904-1967-11628-8
	PII: S}
}

@BOOK{James1981,
  title = {The representation theory of the symmetric group},
  publisher = {Addison-Wesley},
  year = {1981},
  author = {James, G. and Kerber, A.},
  volume = {16},
  series = {Encyclopedia of Mathematics and its Applications},
  journal = {Reading, Mass}
}

@ARTICLE{Jantzen1977,
  author = {Jantzen, Jens C.},
  title = {Kontravariante Formen auf induzierten Darstellungen halbeinfacher
	Lie-Algebren},
  journal = {Mathematische Annalen},
  year = {1977},
  volume = {226},
  pages = {53--65},
  number = {1},
  month = feb,
  file = {:D\:\\eBooks\\papers\\representation\\Jantzen, J. C. Kontravariante Formen auf induzierten Darstellungen halbeinfacher Lie-Algebren.pdf:PDF},
  owner = {hoxide},
  timestamp = {2010.04.24},
  url = {http://dx.doi.org/10.1007/BF01391218}
}

@ARTICLE{Joseph1985,
  author = {Anthony Joseph},
  title = {On the associated variety of a primitive ideal},
  journal = {Journal of Algebra},
  year = {1985},
  volume = {93},
  pages = {509 - 523},
  number = {2},
  doi = {DOI: 10.1016/0021-8693(85)90172-3},
  file = {:D\:\\eBooks\\papers\\representation\\Anthony Joseph, On the associated variety of a primitive ideal.PDF:PDF},
  issn = {0021-8693},
  url = {http://www.sciencedirect.com/science/article/B6WH2-4CWYWG5-3K/2/22f72727e2f07623e98d9023f223e178}
}

@ARTICLE{Kashiwara1978,
  author = {Kashiwara, M. and Vergne, M.},
  title = {On the Segal-Shale-Weil representations and harmonic polynomials},
  journal = {Inventiones Mathematicae},
  year = {1978},
  volume = {44},
  pages = {1--47},
  number = {1},
  month = feb,
  file = {:D\:\\eBooks\\papers\\representation\\M. Kashiwara, M. Vergen On the Segal-Shale-Weil Representations and Harmonic Polynomials.PDF:PDF},
  owner = {hoxide},
  timestamp = {2009.07.23},
  url = {http://dx.doi.org/10.1007/BF01389900}
}

@ARTICLE{Kazhdan1978,
  author = {Kazhdan, D. and Kostant, B. and Sternberg, S.},
  title = {Hamiltonian group actions and dynamical systems of calogero type},
  journal = {Comm. Pure Appl. Math.},
  year = {1978},
  volume = {31},
  pages = {481--507},
  number = {4},
  file = {:D\:\\eBooks\\papers\\representation\\Kazhdan, Kostant, Sternberg, Hamiltonian group actions and dynamical systems of calogero type.PDF:PDF},
  issn = {1097-0312},
  owner = {hoxide},
  publisher = {Wiley Subscription Services, Inc., A Wiley Company},
  timestamp = {2010.10.25},
  url = {http://dx.doi.org/10.1002/cpa.3160310405}
}

@ARTICLE{KimLee2010,
  author = {Kim, Sangjib and Lee, Soo T.},
  title = {Pieri algebras for the orthogonal and symplectic groups},
  year = {2010},
  month = {Mar},
  abstract = {We study the structure of a family of algebras which encodes a generalization
	of the Pieri Rule for the complex orthogonal group. In particular,
	we show that each of these algebras has a standard monomial basis
	and has a flat deformation to a Hibi algebra. There is also a parallel
	theory for the complex symplectic group.},
  archiveprefix = {arXiv},
  citeulike-article-id = {5104107},
  citeulike-linkout-0 = {http://arxiv.org/abs/0907.1336},
  citeulike-linkout-1 = {http://arxiv.org/pdf/0907.1336},
  day = {18},
  eprint = {0907.1336},
  keywords = {branching, law},
  posted-at = {2010-06-23 03:44:31},
  priority = {0},
  url = {http://arxiv.org/abs/0907.1336}
}

@INCOLLECTION{Knapp1983,
  author = {Knapp, A.},
  title = {Minimal K-type formula},
  booktitle = {Non Commutative Harmonic Analysis and Lie Groups},
  publisher = {Springer Berlin Heidelberg},
  year = {1983},
  pages = {107--118},
  abstract = {Without Abstract},
  doi = {10.1007/BFb0071499},
  file = {:D\:\\eBooks\\papers\\representation\\Knapp, Minimal K-type formula.pdf:PDF},
  journal = {Non Commutative Harmonic Analysis and Lie Groups},
  owner = {hoxide},
  timestamp = {2010.07.11},
  url = {http://dx.doi.org/10.1007/BFb0071499}
}

@BOOK{KnappVogan1995,
  title = {Cohomological induction and unitary representations},
  publisher = {Princeton Univ Pr},
  year = {1995},
  author = {Knapp, A.W. and Vogan, D.A.}
}

@BOOK{Knapp1996Lie,
  title = {Lie groups beyond an introduction},
  publisher = {Birkhauser},
  year = {1996},
  author = {Anthony W. Knapp}
}

@ARTICLE{Kostant1975,
  author = {Kostant, Bertram},
  title = {Verma modules and the existence of quasi-invariant differential operators},
  journal = {Non-Commutative Harmonic Analysis},
  year = {1975},
  volume = {466},
  pages = {101--128},
  file = {:D\:\\eBooks\\papers\\representation\\Kostant, Verma modules and the existence of quasi-invariant differential operators.pdf:PDF},
  owner = {hoxide},
  timestamp = {2010.03.12},
  url = {http://dx.doi.org/10.1007/BFb0082201}
}

@ARTICLE{Kostant1969,
  author = {Bertram Kostant},
  title = {On the existence and irreducibility of certain series of representations},
  journal = {Bull. Amer. Math. Soc.},
  year = {1969},
  volume = {75},
  pages = {627-642},
  number = {4},
  file = {:D\:\\eBooks\\papers\\representations\\BERTRAM KOSTANT\\On the existence and irreducibility of certain series of representations.pdf:PDF},
  owner = {hoxide},
  review = {MR0245725},
  timestamp = {2009.05.12},
  url = {http://projecteuclid.org/euclid.bams/1183530620}
}

@ARTICLE{Kostant1963,
  author = {Kostant, Bertram},
  title = {Lie Group Representations on Polynomial Rings},
  journal = {American Journal of Mathematics},
  year = {1963},
  volume = {85},
  pages = {327--404},
  number = {3},
  copyright = {Copyright 1963 The Johns Hopkins University Press},
  file = {:D\:\\eBooks\\papers\\representation\\Kostant, Lie Group Representations on Polynomial Rings.PDF:PDF},
  issn = {00029327},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Jul., 1963},
  publisher = {The Johns Hopkins University Press},
  url = {http://www.jstor.org/stable/2373130}
}

@ARTICLE{Kostant1961,
  author = {Kostant, Bertram},
  title = {Lie Algebra Cohomology and the Generalized Borel-Weil Theorem},
  journal = {The Annals of Mathematics},
  year = {1961},
  volume = {74},
  pages = {329--387},
  number = {2},
  copyright = {Copyright © 1961 Annals of Mathematics},
  file = {:D\:\\eBooks\\papers\\representation\\Kostant, Lie Algebra Cohomology and the Generalized Borel-Weil Theorem.PDF:PDF},
  issn = {0003486X},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Sep., 1961},
  publisher = {Annals of Mathematics},
  series = {Second Series},
  url = {http://www.jstor.org/stable/1970237}
}

@ARTICLE{KostantRallis1971,
  author = {Kostant, B. and Rallis, S.},
  title = {Orbits and Representations Associated with Symmetric Spaces},
  journal = {American Journal of Mathematics},
  year = {1971},
  volume = {93},
  pages = {753--809},
  number = {3},
  copyright = {Copyright 1971 The Johns Hopkins University Press},
  file = {:D\:\\eBooks\\papers\\representation\\Kostant and Rallis, Orbits and Representations Associated with Symmetric Spaces.pdf:PDF},
  issn = {00029327},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Jul., 1971},
  publisher = {The Johns Hopkins University Press}
}

@ARTICLE{KudlaRallis1990,
  author = {Kudla, Stephen and Rallis, Stephen},
  title = {Degenerate principal series and invariant distributions},
  journal = {Israel Journal of Mathematics},
  year = {1990},
  volume = {69},
  pages = {25--45},
  number = {1},
  month = {Feb},
  abstract = {In this article we give a description of the tempered distributions
	on a matrix spaceM m,n(R) which are invariant under the linear action
	of an orthogonal groupO(p, q),p+q=m. We also determine the points
	of reducibility of the degenerate principal series of the metaplectic
	group Mp(n,R) induced from a character of the maximal parabolic with
	GL(n,R) as Levi factor. Finally, we identify the representation of
	MP(n,R) which is associated to the trivial representation ofO(p,
	q) under the archimedean theta correspondence.},
  file = {:D\:\\eBooks\\papers\\representation\\Stephen Kudla, Stephen Rallis, Degenerate principal series and invariant distributions.pdf:PDF},
  owner = {hoxide},
  timestamp = {2010.03.06},
  url = {http://dx.doi.org/10.1007/BF02764727}
}

@ARTICLE{Kudla1986,
  author = {Kudla, Stephen S.},
  title = {On the local theta-correspondence},
  journal = {Inventiones Mathematicae},
  year = {1986},
  volume = {83},
  pages = {229--255},
  number = {2},
  month = jun,
  file = {:D\:\\eBooks\\papers\\representation\\Stephen S. Kudla, On the local theta-correspondence.PDF:PDF;:D\:\\eBooks\\math\\papers\\representations\\Stephen S. Kudla\\On the local theta-correspondence Invent. Math..pdf:PDF},
  owner = {hoxide},
  timestamp = {2009.05.06},
  url = {http://dx.doi.org/10.1007/BF01388961}
}

@ARTICLE{Kumaresan1980,
  author = {Kumaresan, S.},
  title = {On the canonicalk-types in the irreducible unitaryg-modules with
	non-zero relative cohomology},
  journal = {Inventiones Mathematicae},
  year = {1980},
  volume = {59},
  pages = {1--11},
  number = {1},
  month = feb,
  file = {:D\:\\eBooks\\papers\\representation\\S. Kumaresan,On the canonical k-types in the irreducible unitaryg-modules with non-zero relative cohomology.pdf:PDF},
  owner = {hoxide},
  timestamp = {2009.11.19},
  url = {http://dx.doi.org/10.1007/BF01390311}
}

@ARTICLE{LeeZhu1997,
  author = {Lee, Soo and Zhu, Chen-Bo},
  title = {Degenerate principal series and local theta correspondence II},
  journal = {Israel Journal of Mathematics},
  year = {1997},
  volume = {100},
  pages = {29--59},
  number = {1},
  month = dec,
  abstract = {Abstract&nbsp;&nbsp;Following our previous paper [LZ] which deals
	with the groupU(n, n), we study the structure of certain Howe quotients
	惟},
  file = {:D\:\\eBooks\\papers\\representation\\Soo Teck Lee, Chen-bo Zhu, degenerate principal series and local theta correspondence II.PDF:PDF},
  owner = {hoxide},
  timestamp = {2009.08.27},
  url = {http://dx.doi.org/10.1007/BF02773634}
}

@ARTICLE{LeeZhu1998,
  author = {Lee, Soo Teck and Zhu, Chen-Bo},
  title = {Degenerate Principal Series and Local Theta Correspondence},
  journal = {Transactions of the American Mathematical Society},
  year = {1998},
  volume = {350},
  pages = {5017--5046},
  number = {12},
  abstract = {In this paper we determine the structure of the natural $\widetilde{U}(n,n)$
	module Ω p,q(l) which is the Howe quotient corresponding to the determinant
	character $\det ^{l}$ of U(p,q). We first give a description of the
	tempered distributions on Mp+q,n(C) which transform according to
	the character $\det ^{-l}$ under the linear action of U(p,q). We
	then show that after tensoring with a character, Ω p,q(l) can be
	embedded into one of the degenerate series representations of U(n,n).
	This allows us to determine the module structure of Ω p,q(l). Moreover
	we show that certain irreducible constituents in the degenerate series
	can be identified with some of these representations Ω p,q(l) or
	their irreducible quotients. We also compute the Gelfand-Kirillov
	dimensions of the irreducible constituents of the degenerate series.},
  copyright = {Copyright © 1998 American Mathematical Society},
  file = {:D\:\\eBooks\\papers\\representation\\Lee Soo Teck, Zhu Chenbo, Degenerate Principal Series and Local Theta Correspondence.PDF:PDF},
  issn = {00029947},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Dec., 1998},
  publisher = {American Mathematical Society},
  url = {http://www.jstor.org/stable/117757}
}

@ARTICLE{Lepowsky1978,
  author = {J. Lepowsky},
  title = {Minimal K-types for certain representations of real semisimple groups},
  journal = {Journal of Algebra},
  year = {1978},
  volume = {51},
  pages = {173 - 210},
  number = {1},
  doi = {DOI: 10.1016/0021-8693(78)90143-6},
  issn = {0021-8693},
  url = {http://www.sciencedirect.com/science/article/B6WH2-4CWYX26-7S/2/31f1d6dc29bc82dca37d6d6ebfc1ec3d}
}

@ARTICLE{Lepowsky1977470,
  author = {J. Lepowsky},
  title = {Generalized Verma modules, the Cartan-Helgason theorem, and the Harish-Chandra
	homomorphism},
  journal = {Journal of Algebra},
  year = {1977},
  volume = {49},
  pages = {470 - 495},
  number = {2},
  doi = {DOI: 10.1016/0021-8693(77)90253-8},
  file = {:D\:\\eBooks\\papers\\representation\\Lepowsky, Generalized Verma modules, the Cartan-Helgason theorem, and the Harish-Chandra homomorphism.pdf:PDF},
  issn = {0021-8693},
  url = {http://www.sciencedirect.com/science/article/B6WH2-4CRY7YD-39/2/4b6fd1bae17fde95786a9b6d2ad218ff}
}

@ARTICLE{Lepowsky1977492,
  author = {J. Lepowsky},
  title = {A generalization of the Bernstein-Gelfand-Gelfand resolution},
  journal = {Journal of Algebra},
  year = {1977},
  volume = {49},
  pages = {496 - 511},
  number = {2},
  doi = {DOI: 10.1016/0021-8693(77)90254-X},
  file = {:D\:\\eBooks\\papers\\representation\\Lepowsky, A generalization of the Bernstein-Gelfand-Gelfand resolution.pdf:PDF},
  issn = {0021-8693},
  url = {http://www.sciencedirect.com/science/article/B6WH2-4CRY7YD-3B/2/0454a45ab36a03b8f45b9884fd7febea}
}

@ARTICLE{Lepowsky1973,
  author = {Lepowsky, J.},
  title = {Algebraic Results on Representations of Semisimple Lie Groups},
  journal = {Transactions of the American Mathematical Society},
  year = {1973},
  volume = {176},
  pages = {1--44},
  abstract = {Let G be a noncompact connected real semisimple Lie group with finite
	center, and let K be a maximal compact subgroup of G. Let g and f
	denote the respective complexified Lie algebras. Then every irreducible
	representation π of g which is semisimple under f and whose irreducible
	f components integrate to finite-dimensional irreducible representations
	of K is shown to be equivalent to a subquotient of a representation
	of g belonging to the infinitesimal nonunitary principal series.
	It follows that π integrates to a continuous irreducible Hilbert
	space representation of G, and the best possible estimate for the
	multiplicity of any finite-dimensional irreducible representation
	of f in π is determined. These results generalize similar results
	of Harish-Chandra, R. Godement and J. Dixmier. The representations
	of g in the infinitesimal nonunitary principal series, as well as
	certain more general representations of g on which the center of
	the universal enveloping algebra of g acts as scalars, are shown
	to have (finite) composition series. A general module-theoretic result
	is used to prove that the distribution character of an admissible
	Hilbert space representation of G determines the existence and equivalence
	class of an infinitesimal composition series for the representation,
	generalizing a theorem of N. Wallach. The composition series of Weyl-group-related
	members of the infinitesimal nonunitary principal series are shown
	to be equivalent. An expression is given for the infinitesimal spherical
	functions associated with the nonunitary principal series. In several
	instances, the proofs of the above results and related results yield
	simplifications as well as generalizations of certain results of
	Harish-Chandra.},
  copyright = {Copyright 1973 American Mathematical Society},
  file = {:D\:\\eBooks\\papers\\representation\\J. Lepowsky, Algebraic Results on Representations of Semisimple Lie Groups.PDF:PDF},
  issn = {00029947},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Feb., 1973},
  publisher = {American Mathematical Society},
  url = {http://www.jstor.org/stable/1996194}
}

@ARTICLE{LepowskyMcCollum1973,
  author = {Lepowsky, J. and McCollum, G. W.},
  title = {On the Determination of Irreducible Modules by Restriction to a Subalgebra},
  journal = {Transactions of the American Mathematical Society},
  year = {1973},
  volume = {176},
  pages = {45--57},
  abstract = {Let B be an algebra over a field, a a subalgebra of B, and a an equivalence
	class of finite dimensional irreducible a-modules. Under certain
	restrictions, bijections are established between the set of equivalence
	classes of irreducible B-modules containing a nonzero a-primary a-submodule,
	and the sets of equivalence classes of all irreducible modules of
	certain canonically constructed algebras. Related results has been
	obtained by Harsh-Chandra and R. Godement in special cases. The general
	methods and results appear to be useful in the representation theory
	of semisimple Lie groups.},
  copyright = {Copyright 1973 American Mathematical Society},
  file = {:D\:\\eBooks\\papers\\representation\\J. Lepowsky, G. W. McCollum, On the Determination of Irreducible Modules by Restriction to a Subalgebra.PDF:PDF},
  issn = {00029947},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Feb., 1973},
  publisher = {American Mathematical Society},
  url = {http://www.jstor.org/stable/1996195}
}

@ARTICLE{LiJun.1997,
  author = {Li, Jian-Shu},
  title = {Automorphic Forms with Degenerate Fourier Coefficients},
  journal = {American Journal of Mathematics},
  year = {Jun., 1997},
  volume = {119},
  pages = {523--578},
  number = {3},
  abstract = {The main theme of this paper is that singular automorphic forms on
	classical groups are given by theta series liftings. We establish
	several inequalities relating the automorphic multiplicities of a
	given representation and that of its abstract theta lift. Our methods
	allow one to lift noncuspidal, square integrable automorphic forms
	when the dual pair involved is in the stable range. In this way we
	construct new families of singular automorphic forms, many of which
	are clearly unipotent. In fact, starting from one-dimensional representations
	and repeating the procedure (of lifting in the stable range), one
	may obtain all automorphic forms which are quadratic unipotent in
	the sense of Moeglin.},
  file = {:D\:\\eBooks\\papers\\representation\\Li Jian Shu, Automorphic Forms with Degenerate Fourier Coefficients.PDF:PDF},
  issn = {00029327},
  owner = {hoxide},
  publisher = {The Johns Hopkins University Press},
  timestamp = {2010.10.20},
  url = {http://www.jstor.org/stable/25098545}
}

@ARTICLE{Li1990,
  author = {Li, Jian-Shu},
  title = {Theta lifting for unitary representations with nonzero cohomology.},
  journal = {Duke Math. J. },
  year = {1990},
  volume = {61},
  pages = {913-937},
  number = {3},
  abstract = {{Given a dual reductive pair $(G,G')$ inside $Sp=Sp\sb{2n}({\bbfR})$
	in the sense of Howe the Weil representation provides a certain relation
	between the representation theory of $G'$ and the one of G (more
	precisely, between the ones of the inverse images $\tilde G'$ resp.
	$\tilde G$ inside the metaplectic two-fold cover $\tilde Sp$ of $Sp$).
	This paper analyses this local theta lifting between discrete series
	representations of $\tilde G'$ and unitary representations of $\tilde
	G$ with nonvanishing relative Lie algebra cohomology. It is shown
	in the case of irreducible type I reductive dual pairs that if the
	``size'' of $G'$ is not greater than that of G and $\pi'$ is a sufficiently
	regular discrete series representation of $\tilde G'$ then it has
	a nonzero theta lifting to $\tilde G.$ This representation $\theta(\pi')=\pi$
	is a unitary one with nonzero cohomology. Varying $\tilde G'$ one
	obtains a large collection of unitary representations of $\tilde
	G$ with nonzero cohomology and, for $G=SO(n,1)$ or $SU(n,1)$, all
	of them. \par This local result can be used to construct global automorphic
	forms (via global theta lifting) which have cohomological significance,
	i.e. provide nontrivial cohomology classes for certain arithmetic
	cocompact subgroups of $\tilde G.$ This is carried through by the
	author in a yet unpublished paper [Nonvanishing theorems for the
	cohomology of certain arithmetic quotients].}},
  classmath = {{*22E45 (Analytic repres.of Lie and linear algebraic groups over real
	fields) 11F75 (Cohomology of arithmetic groups) 11F27 (Theta series;
	Weil representation) 57T10 (Homology and cohomology of Lie groups)
	}},
  doi = {10.1215/S0012-7094-90-06135-6},
  file = {:D\:\\eBooks\\papers\\representation\\Li Jianshu, Theta lifting for unitary representations with nonzero cohomology.pdf:PDF;:D\:\\eBooks\\papers\\representation\\Li Jianshu, Theta lifting for unitary representations with nonzero cohomology.djvu:Djvu},
  keywords = {{dual reductive pair; Weil representation; metaplectic two-fold cover;
	local theta lifting; discrete series representations; unitary representations;
	relative Lie algebra cohomology; global automorphic forms; arithmetic
	cocompact subgroups}},
  language = {English},
  reviewer = {{J.Schwermer (Eichst\"att)}}
}

@ARTICLE{Li1989,
  author = {Li, Jian-Shu},
  title = {Singular unitary representations of classical groups},
  journal = {Inventiones Mathematicae},
  year = {1989},
  volume = {97},
  pages = {237--255},
  number = {2},
  month = jun,
  file = {:D\:\\eBooks\\papers\\representation\\Jian Shu Li, Singular uniatry representations of classical groups.PDF:PDF},
  owner = {hoxide},
  timestamp = {2009.09.22},
  url = {http://dx.doi.org/10.1007/BF01389041}
}

@ARTICLE{LiTanZhu2001,
  author = {Jian-Shu Li and Eng-Chye Tan and Chen-Bo Zhu},
  title = {Tensor Product of Degenerate Principal Series and Local Theta Correspondence},
  journal = {Journal of Functional Analysis},
  year = {2001},
  volume = {186},
  pages = {381 - 431},
  number = {2},
  doi = {DOI: 10.1006/jfan.2001.3786},
  file = {:D\:\\eBooks\\papers\\representation\\Li Jianshu, Eng-Chye, Tan, Zhu Chenbo, Tensor Product of Degenerate Principal Series and Local Theta Correspondence.PDF:PDF},
  issn = {0022-1236},
  keywords = {degenerate principal series; reductive dual pair; local theta correspondence;
	zeta integral; complementary series},
  url = {http://www.sciencedirect.com/science/article/B6WJJ-457D572-53/2/2039a7741a194ad07ef59fdadbbf4da6}
}

@ARTICLE{Loke2008,
  author = {Hung Yean Loke and Gordan Savin},
  title = {Dual pair correspondences for non-linear covers of orthogonal groups},
  journal = {Journal of Functional Analysis},
  year = {2008},
  volume = {255},
  pages = {184 - 199},
  number = {1},
  abstract = {In this paper we study compact dual pair correspondences arising from
	smallest representations of non-linear covers of odd orthogonal groups.
	We identify representations appearing in these correspondences with
	subquotients of cohomologically induced representations.},
  doi = {DOI: 10.1016/j.jfa.2008.04.009},
  file = {:D\:\\eBooks\\papers\\representation\\Loke, Savin, Dual pair correspondences for non-linear covers of odd orthogonal groups.pdf:PDF},
  issn = {0022-1236},
  keywords = {Lie groups},
  url = {http://www.sciencedirect.com/science/article/B6WJJ-4SGTM8T-5/2/2698737c1f58390dfd129f4561129d0a}
}

@ARTICLE{LokeSavin2008,
  author = {Hung Yean Loke and Gordan Savin},
  title = {The Smallest Representations of Nonlinear Covers of Odd Orthogonal
	Groups},
  journal = {American Journal of Mathematics},
  year = {2008},
  volume = {130},
  pages = {pp. 763-797},
  number = {3},
  abstract = {We construct the smallest genuine representations of a nonlinear cover
	of the group SO°(p, q) where p + q is odd. We determine correspondences
	of infinitesimal characters arising from restricting the smallest
	representations to dual pairs so(p,a) ⊕ so(b) where a + b = q.},
  copyright = {Copyright © 2008 The Johns Hopkins University Press},
  file = {:D\:\\eBooks\\papers\\representation\\Hung Yean Loke and Gordan Savin, The Smallest Representations of Nonlinear Covers of Odd Orthogonal Groups.PDF:PDF},
  issn = {00029327},
  jstor_articletype = {research-article},
  jstor_formatteddate = {Jun., 2008},
  language = {English},
  publisher = {The Johns Hopkins University Press},
  url = {http://www.jstor.org/stable/40068146}
}

@ARTICLE{1953,
  author = {Mackey, George W.},
  title = {Induced Representations of Locally Compact Groups II. The Frobenius
	Reciprocity Theorem},
  journal = {The Annals of Mathematics},
  year = {1953},
  volume = {58},
  pages = {193--221},
  number = {2},
  copyright = {Copyright 1953 Annals of Mathematics},
  file = {:D\:\\eBooks\\papers\\representation\\George W. Mackey, Induced Representations of Locally Compact Groups II.PDF:PDF},
  issn = {0003486X},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Sep., 1953},
  publisher = {Annals of Mathematics},
  series = {Second Series},
  url = {http://www.jstor.org/stable/1969786}
}

@ARTICLE{Mackey1952,
  author = {Mackey, George W.},
  title = {Induced Representations of Locally Compact Groups I},
  journal = {The Annals of Mathematics},
  year = {1952},
  volume = {55},
  pages = {101--139},
  number = {1},
  copyright = {Copyright 漏 1952 Annals of Mathematics},
  file = {:D\:\\eBooks\\papers\\representation\\George W. Mackey, Induced Representations of Locally Compact Groups I.PDF:PDF},
  issn = {0003486X},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Jan., 1952},
  publisher = {Annals of Mathematics},
  series = {Second Series},
  url = {http://www.jstor.org/stable/1969423}
}

@ARTICLE{Martin1975,
  author = {Martin, Robert Paul},
  title = {On the Decomposition of Tensor Products of Principal Series Representations
	for Real-Rank One Semisimple Groups},
  journal = {Transactions of the American Mathematical Society},
  year = {1975},
  volume = {201},
  pages = {177--211},
  abstract = {Let G be a connected semisimple real-rank one Lie group with finite
	center. It is shown that the decomposition of the tensor product
	of two representations from the principal series of G consists of
	two pieces, Tc and Td, where Tc is a continuous direct sum with respect
	to Plancherel measure on G of representations from the principal
	series only, occurring with explicitly determined multiplicities,
	and Td is a discrete sum of representations from the discrete series
	of G, occurring with multiplicities which are, for the present, undetermined.},
  copyright = {Copyright 1975 American Mathematical Society},
  file = {:D\:\\eBooks\\papers\\representation\\Martin, On the Decomposition of Tensor Products of Principal Series Representations.pdf:PDF},
  issn = {00029947},
  jstor_formatteddate = {Jan., 1975},
  publisher = {American Mathematical Society}
}

@ARTICLE{1963,
  author = {Matsushima, Yozo and Murakami, Shingo},
  title = {On Vector Bundle Valued Harmonic Forms and Automorphic Forms on Symmetric
	Riemannian Manifolds},
  journal = {The Annals of Mathematics},
  year = {1963},
  volume = {78},
  pages = {365--416},
  number = {2},
  copyright = {Copyright 1963 Annals of Mathematics},
  file = {:D\:\\eBooks\\papers\\representation\\Matsushima, Yozo and Murakami, Shingo, On Vector Bundle Valued Harmonic Forms and Automorphic Forms on Symmetric Riemannian Manifolds.PDF:PDF},
  issn = {0003486X},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Sep., 1963},
  publisher = {Annals of Mathematics},
  series = {Second Series},
  url = {http://www.jstor.org/stable/1970348}
}

@ARTICLE{Matumoto1987,
  author = {Matumoto, Hisayosi},
  title = {Whittaker vectors and associated varieties},
  journal = {Inventiones Mathematicae},
  year = {1987},
  volume = {89},
  pages = {219-224},
  note = {10.1007/BF01404678},
  affiliation = {Department of Mathematics Masachusetts Institute of Technology 02139
	Cambridge MA USA},
  issn = {0020-9910},
  issue = {1},
  keyword = {Mathematics and Statistics},
  publisher = {Springer Berlin / Heidelberg},
  url = {http://dx.doi.org/10.1007/BF01404678}
}

@ARTICLE{Moeglin1989,
  author = {C. Moeglin},
  title = {Correspondance de Howe pour les paires reductives duales: Quelques
	calculs dans le cas archimedien},
  journal = {Journal of Functional Analysis},
  year = {1989},
  volume = {85},
  pages = {1 - 85},
  number = {1},
  doi = {DOI: 10.1016/0022-1236(89)90046-3},
  file = {:D\:\\eBooks\\papers\\representation\\C. Moeglin, Correspondance de Howe pour les paires reductives duales, Quelques calculs dans le cas archimedien.pdf:PDF},
  issn = {0022-1236},
  url = {http://www.sciencedirect.com/science/article/B6WJJ-4D8DY9P-FG/2/748c687276c8b0d4c642cf3f888913b2}
}

@ARTICLE{NishiyammaOchiaiZhu2006,
  author = {K. Nishiyama and H. Ochiai and Zhu Chen-Bo},
  title = {Theta lifting of nilpotent orbits for symmetric pairs},
  journal = {Trans. Amer. Math. Soc.},
  year = {2006},
  volume = {358},
  pages = {2713-2734},
  number = {6},
  file = {:D\:\\eBooks\\papers\\representation\\Nishiyama, Ochiai, Zhu Chenbo,Theta lifting of nilpotent orbits for symmetric pairs.PDF:PDF},
  owner = {hoxide},
  timestamp = {2010.10.26}
}

@ARTICLE{NishyamaZhu2004,
  author = {Kyo Nishiyama and Chen-Bo Zhu},
  title = {Theta lifting of unitary lowest weight modules and their associated
	cycles},
  journal = {Duke Math. J. },
  year = {2004},
  volume = {125},
  pages = {415-465},
  number = {3},
  abstract = {{Consider reductive dual pairs of the form $(G,G')=(O(p,q),Sp(2n,\Bbb
	R)),(U(p,q),U(m,n))$ and $(Sp(p,q),O^*(2n))$ in the stable range,
	with $G'$ the smaller member. In this paper, the authors study the
	theta lifts of unitary lowest weight modules of $G'$, in particular
	the geometry of their associated varieties. Since by {\it J.-S. Li}
	[Invent. Math. 97, No.2, 237-255 (1989; Zbl 0694.22011)], unitarity
	is preserved by the Howe correspondence in the stable range, these
	are (very singular) unitary representations of $G$. \par Let $\germ
	g=\germ k \oplus \germ s$ and $\germ g'=\germ k' \oplus \germ s'$
	be the Cartan decompositions of the complexified Lie algebras of
	$G$ and $G'$, respectively. For any nilpotent $K'_{\Bbb C}$-orbit
	$\Cal O'$ in $\germ s'$, {\it K. Nishiyama, H. Ochiai} and {\it C.-B.
	Zhu} [Theta lifting of nilpotent orbits for symmetric pairs, Trans.
	Am. Math. Soc., to appear] have defined in a natural way the theta
	lift $\theta(\Cal O')$, a nilpotent $K_{\Bbb C}$-orbit in $\germ
	s$. If $\pi'$ is a unitary lowest weight module of $G'$ then its
	associated variety $\Cal {AV}(\pi')$ consists of the closure of a
	single such orbit, and its associated cycle $\Cal {AC}(\pi')$ must
	be an integral multiple thereof. The main result is that the associated
	variety of the theta lift of $\pi'$ is the theta lift of the associated
	variety of $\pi'$, and the multiplicity in the associated cycles
	is preserved under the lifting. Moreover, a formula for this multiplicity
	is given. If (as is almost always the case) $\pi'$ occurs in the
	correspondence for a dual pair $(G(k),G')$ with $G(k)$ compact as
	the theta lift of a representation $\sigma$ of $G(k)$, then this
	is a simple formula in terms of the dimension of $\sigma$. Generalizing
	the first part of the theorem, the authors show that if $\rho'$ is
	any irreducible admissible (not necessarily unitary) representation
	of $G'$ whose associated variety is irreducible (hence the closure
	of a single nilpotent orbit $\Cal O'$), then the associated variety
	of the theta lift of $\rho'$ is contained in the closure of $\theta(\Cal
	O')$. \par In addition, back in the setting of $\pi'$ a unitary lowest
	weight module with theta lift $\pi$, the authors obtain a formula
	for the $K$-structure of $\pi$ in terms of the $K'$-structure of
	$\pi'$.}},
  classmath = {{*22E46 (Semi-simple Lie groups and their representations) 11F27 (Theta
	series; Weil representation) }},
  doi = {10.1215/S0012-7094-04-12531-X},
  file = {:D\:\\eBooks\\papers\\representation\\Nishiyama, Zhu Chen Bo, Theta lifting of unitary lowest weight modules and their associated cycles.PDF:PDF},
  keywords = {Howe correspondence; nilpotent orbits; associated varieties; associated
	cycles; singular unitary representations},
  language = {English},
  reviewer = {{Annegret Paul (Kalamazoo)}}
}

@ARTICLE{Parthasarathy1980,
  author = {Parthasarathy, R},
  title = {Criteria for the unitarizability of some highest weight modules},
  journal = {Proceedings Mathematical Sciences},
  year = {1980},
  volume = {89},
  pages = {1--24},
  number = {1},
  month = jan,
  abstract = {Abstract&nbsp;&nbsp;For a linear semisimple Lie group we obtain a
	necessary and sufficient condition for a highest weight module with
	non-singular infinitesimal character to be unitarizable.},
  file = {:D\:\\eBooks\\papers\\representation\\R. Rapthasarathy, CRITERIA FOR THE UNITARIZABILITY OF SOME HIGHEST WEIGHT MODULES.pdf:PDF},
  owner = {hoxide},
  timestamp = {2009.11.18},
  url = {http://dx.doi.org/10.1007/BF02881021}
}

@ARTICLE{2000,
  author = {Paul, Annegret},
  title = {Howe Correspondence for Real Unitary Groups II},
  journal = {Proceedings of the American Mathematical Society},
  year = {2000},
  volume = {128},
  pages = {3129--3136},
  number = {10},
  abstract = {A previous paper by the author describes the Howe correspondence for
	dual pairs of the form (U (p, q), U (r, s)) with p + q = r + s, in
	terms of Langlands parameters. We extend these results to the case
	p + q = r + s + 1.},
  copyright = {Copyright 2000 American Mathematical Society},
  file = {:D\:\\eBooks\\papers\\representation\\Annegret Paul, Howe Correspondence for Real Unitary Groups II.pdf:PDF},
  issn = {00029939},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Oct., 2000},
  publisher = {American Mathematical Society},
  url = {http://www.jstor.org/stable/2669186}
}

@ARTICLE{Paul1998384,
  author = {Annegret Paul},
  title = {Howe Correspondence for Real Unitary Groups},
  journal = {Journal of Functional Analysis},
  year = {1998},
  volume = {159},
  pages = {384 - 431},
  number = {2},
  abstract = {Roger Howe proved that for any reductive dual pair (G,G') in the symplectic
	groupSp(2n,?, there is a one-to-one correspondence of irreducible
	admissible representations of some two-fold covers of G and G'. We
	determine this correspondence explicitly for dual pairs of the form
	(U(p,q),U(r,s)) withr+s=p+q, and describe it in terms of Langlands
	parameters. In this case, the correspondence may be understood in
	a natural way as a correspondence of representations of the linear
	groups, rather than the appropriate covers. We show that every irreducible
	admissible representation ofU(p,q) occurs in the correspondence with
	precisely one unitary group of equal rank. This result verifies a
	conjecture of Harris, Kudla, and Sweet, who investigated the correspondence
	for unitary groups of equal size overp-adic fields. The correspondence
	of discrete series representations was determined by J.-S. Li. For
	induced representations, the correspondence is obtained in a natural
	way from the corresponding discrete series on the respective Levi
	factors of the parabolic subgroups ofU(p,q) andU(r,s). Generalizing
	a result of Li, we show that under the correspondence representations
	with nonzero cohomology are matched in an interesting way, with unitarity
	not necessarily preserved. The proof uses the induction principle
	which is due to Kudla, and an argument involvingK-types and the space
	of joint harmonics (Howe).},
  doi = {DOI: 10.1006/jfan.1998.3330},
  file = {:D\:\\eBooks\\papers\\representation\\Annegret Paul, Howe Correspondence for Real Unitary Groups.pdf:PDF},
  issn = {0022-1236},
  url = {http://www.sciencedirect.com/science/article/B6WJJ-45JCC00-4/2/a2c1d0bf0a742f730da7d8f6f3a5c86c}
}

@ARTICLE{Paul2002129,
  author = {Annegret Paul and Peter E. Trapa},
  title = {One-Dimensional Representations of U (p,q) and the Howe Correspondence},
  journal = {Journal of Functional Analysis},
  year = {2002},
  volume = {195},
  pages = {129 - 166},
  number = {1},
  abstract = {We explicitly determine the theta lifts of all one-dimensional representations
	of U (p,q) in terms of Langlands parameters, and determine exactly
	which lifts are unitary. Moreover, we show that such a lift is unitary
	if and only if it is a weakly fair derived functor module of the
	form Aq([lambda]). Finally, we show that the correspondence of unitary
	representations behaves well with respect to associated cycles.},
  doi = {DOI: 10.1006/jfan.2002.3974},
  file = {:D\:\\eBooks\\papers\\representation\\Annegret Paul, One-Dimensional Representations of U (p,q) and the Howe Correspondence.pdf:PDF},
  issn = {0022-1236},
  url = {http://www.sciencedirect.com/science/article/B6WJJ-478RYBM-6/2/6d12c62814b882430bf55c59e280ab6a}
}

@ARTICLE{Pedroza20071493,
  author = {Andres Pedroza and Loring W. Tu},
  title = {On the localization formula in equivariant cohomology},
  journal = {Topology and its Applications},
  year = {2007},
  volume = {154},
  pages = {1493 - 1501},
  number = {7},
  note = {Special Issue: The Third Joint Meeting Japan-Mexico in Topology and
	its Applications},
  abstract = {We give a generalization of the Atiyah-Bott-Berline-Vergne localization
	theorem for the equivariant cohomology of a torus action. We replace
	the manifold having a torus action by an equivariant map of manifolds
	having a compact connected Lie group action. This provides a systematic
	method for calculating the Gysin homomorphism in ordinary cohomology
	of an equivariant map. As an example, we recover a formula of Akyildiz-Carrell
	for the Gysin homomorphism of flag manifolds.},
  doi = {DOI: 10.1016/j.topol.2005.10.013},
  file = {:D\:\\eBooks\\papers\\representation\\Andres Pedroza and Loring W. Tu, On the localization formula in equivariant cohomology.PDF:PDF},
  issn = {0166-8641},
  keywords = {Atiyah-Bott-Berline-Vergne localization formula},
  url = {http://www.sciencedirect.com/science/article/B6V1K-4M69JB4-5/2/478712bd82f7fda3f0c73bce92a59ce8}
}

@ARTICLE{Przebinda1996,
  author = {T. Przebinda},
  title = {The duality correspondence of infinitesimal characters},
  journal = {Colloquium Mathematicum},
  year = {1996},
  volume = {70},
  pages = {93-102},
  file = {:D\:\\eBooks\\papers\\representation\\T. Przebinda, the duality correspondence of infinitesimal characters.pdf:PDF},
  owner = {hoxide},
  timestamp = {2009.08.27}
}

@ARTICLE{Przebinda1988160,
  author = {Tomasz Przebinda},
  title = {On Howe's Duality theorem},
  journal = {Journal of Functional Analysis},
  year = {1988},
  volume = {81},
  pages = {160 - 183},
  number = {1},
  abstract = {We adopt the Langlands classification to the context of real reductive
	dual pairs and prove that Howe's Duality Correspondence maps hermitian
	representations to hermitian representations.},
  doi = {DOI: 10.1016/0022-1236(88)90116-4},
  file = {:D\:\\eBooks\\papers\\representation\\T. Przebinda, On Howe's Duality theorem.pdf:PDF},
  issn = {0022-1236},
  url = {http://www.sciencedirect.com/science/article/B6WJJ-4CTN2TB-1S/2/65e1b7b455cd9f6a59ac8943781151cc}
}

@ARTICLE{Rao1993,
  author = {Ranga Rao, R.},
  title = {On some explicit formulas in the theory of Weil representation.},
  journal = {Pac. J. Math. },
  year = {1993},
  volume = {157},
  pages = {335-371},
  number = {2},
  abstract = {{Let $W$ be the finite subgroup of the symplectic group $Sp(X)$ consisting
	of all $\sigma$ such that $\{e\sb i, e\sb i\sp*\}\subseteq \{\pm
	e\sb i, \pm e\sb i\sp*\}$ for each $i$, where $e\sb i$, $e\sb j\sp*$
	form a symplectic basis of $X= V+V\sp*$. Then using the Bruhat decomposition
	$Sp(X)= PWP$ (where $P$ is the stabilizer of $V\sp*$) the author
	shows the existence of the Haar measures $\mu\sb \sigma$ such that
	for the operators $\xi(\cdot)$; $\xi(p\sb 1 \sigma p\sb 2)= \xi(p\sb
	1) \xi(\sigma) \xi(p\sb 2)$ and $\xi(\sigma\sb 1 \sigma\sb 2)= \xi(\sigma\sb
	1) \xi(\sigma\sb 2)$, $\sigma\sb 1,\sigma\sb 2\in W$, $p\sb 1, p\sb
	2\in P$. For the standard model of $\mu$ he describes the 2-cocycle
	$c(\sigma\sb 1, \sigma\sb 2)$ (the Weil index of the Leray invariant
	of the Lagrangian subspaces $V\sp*$, $V\sp* \sigma\sb 2\sp{-1}$,
	$V\sp* \sigma\sb{1\cdot}$) in terms of the Leray invariant, and generalizes
	the Weil formula for triplets of elements belonging to the big Bruhat
	cell. The author finds the normalizing constant such that the standard
	model is metaplectic and gives the explicit formula for the corresponding
	mutiplier $c(\sigma\sb 1,\sigma\sb 2)$.}},
  classmath = {{*37J99 (Finite-dimensional Hamiltonian etc. systems) 20H15 (Other
	geometric groups, including crystallographic groups) }},
  file = {:D\:\\eBooks\\papers\\representation\\Ranga Rao, On some explicit formulas in the theory of Weil representation.pdf:PDF;:D\:\\eBooks\\papers\\representation\\Ranga Rao, On some explicit formulas in the theory of Weil representation.djvu:Djvu},
  keywords = {{Lagrangian space; symplectic group; Leray invariant; Bruhat cell}},
  language = {English},
  reviewer = {{St.Janeczko (Warszawa)}}
}

@ARTICLE{Repka1979,
  author = {Repka, Joe},
  title = {Tensor products of holomorphic discrete series representations.},
  journal = {Can. J. Math. },
  year = {1979},
  volume = {31},
  pages = {836-844},
  classmath = {{*22E45 (Analytic repres.of Lie and linear algebraic groups over real
	fields) }},
  keywords = {{TENSOR PRODUCTS; HOLOMORPHIC DISCRETE SERIES REPRESENTATIONS}},
  language = {English}
}

@ARTICLE{Repka1976tensor,
  author = {Repka, J.},
  title = {Tensor products of unitary representations of SL2 (R)},
  journal = {AMERICAN MATHEMATICAL SOCIETY},
  year = {1976},
  volume = {82},
  number = {6},
  file = {:D\:\\eBooks\\papers\\representation\\Joe Repka, Tensor products of unitary representations of SL2 (R).pdf:PDF}
}

@ARTICLE{Rocha1983,
  author = {Rocha-Caridi, Alvany and Wallach, Nolan R.},
  title = {Highest Weight Modules Over Graded Lie Algebras: Resolutions, Filtrations
	and Character Formulas},
  journal = {Transactions of the American Mathematical Society},
  year = {1983},
  volume = {277},
  pages = {133--162},
  number = {1},
  abstract = {In this paper the study of multiplicities in Verma modules for Kac-Moody
	algebras is inititated. Our analysis comprises the case when the
	integral root system is Euclidean of rank two. Complete results are
	given in the case of rank two, Kac-Moody algebras, affirming the
	Kazhdan-Lusztig conjectures for the case of infinite dihedral Coxeter
	groups. The main tools in this paper are the resolutions of standard
	modules given in [21] and a generalization to the case of Kac-Moody
	Lie algebras of Jantzen's character sum formula for a quotient of
	two Verma modules (one of the main results of this article). Finally,
	a precise analogy is drawn between the rank two, Kac-Moody algebras
	and the Witt algebra (the Lie algebra of vector fields on the circle).},
  copyright = {Copyright Â© 1983 American Mathematical Society},
  file = {:D\:\\eBooks\\papers\\representation\\Rocha-Caridi,Wallach, Highest Weight Modules Over Graded Lie Algebras Resolutions, Filtrations and Character Formulas.pdf:PDF},
  issn = {00029947},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {May, 1983},
  publisher = {American Mathematical Society},
  url = {http://www.jstor.org/stable/1999349}
}

@ARTICLE{Rossmann1978,
  author = {Rossmann, Wulf},
  title = {Kirillov's character formula for reductive Lie groups},
  journal = {Inventiones Mathematicae},
  year = {1978},
  volume = {48},
  pages = {207-220},
  note = {10.1007/BF01390244},
  affiliation = {Queen's University K7L 3N6 Kingston Ontario Canada},
  file = {:D\:\\eBooks\\papers\\representation\\Wulf Rossmann, Kirillov's character formula for reductive Lie groups.PDF:PDF},
  issn = {0020-9910},
  issue = {3},
  keyword = {Mathematics and Statistics},
  publisher = {Springer Berlin / Heidelberg},
  url = {http://dx.doi.org/10.1007/BF01390244}
}

@ARTICLE{HottaWallach1975,
  author = {Rotta, R. and Wallach, N.R.},
  title = {On Matsushima's formula for the betti numbers of a locally symmetric
	space},
  journal = {Osaka J. Math.},
  year = {1975},
  volume = {12},
  pages = {419-431},
  file = {:D\:\\eBooks\\papers\\representation\\R. Hotta, N. R. Wallach, On Matsushima's formula for the Betti numbers of a locally symmetric space.pdf:PDF},
  owner = {hoxide},
  timestamp = {2010.03.24}
}

@ARTICLE{Sahi1992,
  author = {Sahi, Siddhartha},
  title = {Explicit Hilbert spaces for certain unipotent representations},
  journal = {Inventiones Mathematicae},
  year = {1992},
  volume = {110},
  pages = {409--418},
  number = {1},
  month = dec,
  abstract = {Summary LetG be the universal cover of the group of automorphisms
	of a symmetric tube domain and letP=LN be its Shilov boundary parabolic
	subgroup. This paper attaches an irreducible unitary representation
	ofG to each of the (finitely many)L-orbits onn*.},
  file = {:D\:\\eBooks\\papers\\representation\\Sahi S., Explicit Hilbert spaces for certain unipotent representations.pdf:PDF},
  owner = {hoxide},
  timestamp = {2010.07.11},
  url = {http://dx.doi.org/10.1007/BF01231340}
}

@ARTICLE{Sahi1990,
  author = {Sahi, Siddhartha and Stein, Elias M.},
  title = {Analysis in matrix space and Speh's representations},
  journal = {Inventiones Mathematicae},
  year = {1990},
  volume = {101},
  pages = {379--393},
  number = {1},
  month = dec,
  file = {:D\:\\eBooks\\papers\\representation\\Sahi, Stein, Analysis in matrix space and Speh's representations.pdf:PDF},
  owner = {hoxide},
  timestamp = {2010.07.09},
  url = {http://dx.doi.org/10.1007/BF01231507}
}

@ARTICLE{1998,
  author = {Salamanca-Riba, Susana A. and Vogan, David A.},
  title = {On the Classification of Unitary Representations of Reductive Lie
	Groups},
  journal = {The Annals of Mathematics},
  year = {1998},
  volume = {148},
  pages = {1067--1133},
  number = {3},
  copyright = {Copyright 1998 Annals of Mathematics},
  file = {:D\:\\eBooks\\papers\\representation\\Susana A. Salamanca-Riba, David A. Vogan, On the Classification of Unitary Representations of Reductive Lie Groups.pdf:PDF},
  issn = {0003486X},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Nov., 1998},
  publisher = {Annals of Mathematics},
  series = {Second Series}
}

@ARTICLE{Salmasian2007,
  author = {Salmasian, Hadi},
  title = {A notion of rank for unitary representations of reductive groups
	based on Kirillov's orbit method},
  journal = {Duke Math. J. },
  year = {2007},
  volume = {136},
  pages = {1-49},
  number = {1},
  abstract = {{The rank of irreducible unitary representations of semisimple groups
	was first introduced by R. Howe to characterize the `size' of the
	infinite-dimensional representations. In this paper, the author introduces
	a new notion of rank for irreducible unitary representations of semisimple
	groups which is based on Kirillov's method of coadjoint orbits for
	nilpotent groups.}},
  classmath = {{*22E46 (Semi-simple Lie groups and their representations) 22E50 (Repres.
	of Lie and linear algebraic groups over local fields) 11F27 (Theta
	series; Weil representation) }},
  doi = {10.1215/S0012-7094-07-13611-1},
  file = {:D\:\\eBooks\\papers\\representation\\Hadi Salmasian, A notion of rank for unitary representations of reductive groups based on Kirillov's orbit method.pdf:PDF},
  keywords = {{rank; unitary representations; reductive groups; orbit method}},
  language = {English},
  reviewer = {{Benjamin Cahen (Metz)}}
}

@ARTICLE{Schmid1969,
  author = {Schmid, Wilfried},
  title = {Die Randwerte holomorpher Funktionen auf hermitesch symmetrischen
	R\"aumen},
  journal = {Inventiones Mathematicae},
  year = {1969},
  volume = {9},
  pages = {61--80},
  number = {1},
  month = mar,
  file = {:D\:\\eBooks\\papers\\representation\\Wilfried schmid, Die Randwerte holomorpher Funktionen auf hermitesch symmetrischen raumen.pdf:PDF},
  owner = {hoxide},
  timestamp = {2009.10.12},
  url = {http://dx.doi.org/10.1007/BF01389889}
}

@ARTICLE{Schmid2000,
  author = {Schmid, Wilfried and Vilonen, Kari},
  title = {Characteristic Cycles and Wave Front Cycles of Representations of
	Reductive Lie Groups},
  journal = {The Annals of Mathematics},
  year = {2000},
  volume = {151},
  pages = {pp. 1071-1118},
  number = {3},
  copyright = {Copyright © 2000 Annals of Mathematics},
  file = {:D\:\\eBooks\\papers\\representation\\Schmid, Characteristic Cycles and Wave Front Cycles of Representations of Reductive Lie Groups.PDF:PDF},
  issn = {0003486X},
  jstor_articletype = {research-article},
  jstor_formatteddate = {May, 2000},
  language = {English},
  publisher = {Annals of Mathematics},
  series = {Second Series},
  url = {http://www.jstor.org/stable/121129}
}

@ARTICLE{1962,
  author = {Shale, David},
  title = {Linear Symmetries of Free Boson Fields},
  journal = {Transactions of the American Mathematical Society},
  year = {1962},
  volume = {103},
  pages = {149--167},
  number = {1},
  copyright = {Copyright 1962 American Mathematical Society},
  file = {:D\:\\eBooks\\papers\\representation\\david shale, linear symmetries of free boson fields.pdf:PDF},
  issn = {00029947},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Apr., 1962},
  publisher = {American Mathematical Society},
  url = {http://www.jstor.org/stable/1993745}
}

@ARTICLE{Shimura1990,
  author = {Shimura, Goro},
  title = {Invariant Differential Operators on Hermitian Symmetric Spaces},
  journal = {The Annals of Mathematics},
  year = {1990},
  volume = {132},
  pages = {237--272},
  number = {2},
  copyright = {Copyright © 1990 Annals of Mathematics},
  file = {:D\:\\eBooks\\papers\\representation\\Shimura, Invariant Differential Operators on Hermitian Symmetric Spaces.pdf:PDF},
  issn = {0003486X},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Sep., 1990},
  publisher = {Annals of Mathematics},
  series = {Second Series},
  url = {http://www.jstor.org/stable/1971523}
}

@ARTICLE{Speh1983,
  author = {Speh, Birgit},
  title = {Unitary representations ofGl(n, IR) with non-trivial (g,K)-cohomology},
  journal = {Inventiones Mathematicae},
  year = {1983},
  volume = {71},
  pages = {443--465},
  number = {3},
  month = mar,
  file = {:D\:\\eBooks\\papers\\representation\\Birgit Speh, Unitary Representations of GL(n,R) with Non-trivial (g,K)-cohomology.pdf:PDF},
  owner = {hoxide},
  timestamp = {2010.04.20},
  url = {http://dx.doi.org/10.1007/BF02095987}
}

@ARTICLE{Speh1980,
  author = {Birgit Speh and David Vogan},
  title = {Reducibility of generalized principal series representations},
  journal = {Acta Mathematica},
  year = {1980},
  volume = {145},
  pages = {227--299},
  number = {1},
  month = {Dec},
  file = {:D\:\\eBooks\\papers\\representation\\Bright Speh and David Vogan, Reducibility of generalized principal series representations.pdf:PDF},
  owner = {hoxide},
  timestamp = {2010.02.20},
  url = {http://dx.doi.org/10.1007/BF02414191}
}

@ARTICLE{Sun2007,
  author = {Sun,Binyong},
  title = {Matrix coefficients of cohomologically induced representations},
  journal = {Compositio Mathematica},
  year = {2007},
  volume = {143},
  pages = {201-221},
  number = {01},
  abstract = {ABSTRACT We define integral formulas which produce certain matrix
	coefficients of cohomologically induced representations of real reductive
	groups. They are analogous to Harish-Chandra&apos;s Eisenstein integrals
	for matrix coefficients of ordinary induced representations, and
	generalize Flensted-Jensen&apos;s fundamental functions for discrete
	series.},
  doi = {10.1112/S0010437X06002508},
  eprint = {http://journals.cambridge.org/article_S0010437X06002508},
  file = {:D\:\\eBooks\\papers\\representation\\Sun Binyong, Matrix coeffcients of cohomologically induced representations.pdf:PDF},
  url = {http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=653820&fulltextType=RA&fileId=S0010437X06002508}
}

@ARTICLE{Tilgner1977,
  author = {Hans Tilgner},
  title = {A graded generalization of Lie triples},
  journal = {Journal of Algebra},
  year = {1977},
  volume = {47},
  pages = {190 - 196},
  number = {1},
  abstract = {A graded generalization of Lie triples is defined such that the well-known
	relations between Lie triples and Lie algebras remain valid. For
	instance, the graded generalizations of Lie algebras, considered
	recently in physics and mathematics, become such triples with respect
	to the graded double commutator, and every such triple can be constructed
	by means of an involutive automorphism of degree zero on such an
	algebra as eigenspace of eigenvalue -1. In case of a Z2-graduation
	there is an elementary example, considered first in the second quantization
	in quantum field theory, which is constructed on a graded vector
	space V with a graded symmetric bilinear form <, >. This triple has
	a realization in the Clifford algebra constructed over (V, <, >).
	An elementary construction of representations which in the (Lie)
	group case leads to inhomogenizations and tangent groups can be generalized
	to these triples as well.},
  doi = {DOI: 10.1016/0021-8693(77)90219-8},
  file = {:D\:\\eBooks\\papers\\representation\\Hans tilgner, a graded generalization of lie triples.PDF:PDF},
  issn = {0021-8693},
  url = {http://www.sciencedirect.com/science/article/B6WH2-4CRY7P1-19/2/3de582c6b9b555387ef9f4c974ef2de8}
}

@ARTICLE{Tilgner1977163,
  author = {Hans Tilgner},
  title = {Graded generalizations of Weyl- and Clifford algebras},
  journal = {Journal of Pure and Applied Algebra},
  year = {1977},
  volume = {10},
  pages = {163 - 168},
  number = {2},
  abstract = {Graded skew bilinear forms {,} on graded vector spaces V are defined
	such that their restrictions to the even resp. odd subspaces are
	skew resp. odd. Over such graded symplectic vector spaces a (universal)
	factor algebra of the tensor algebra of V is described which reduces
	to a Weyl- resp. Clifford algebra if only one even resp. odd subspace
	is nontrivial. Introducing the total graduation on this polynomial
	algebra and graded symmetrization it is shown that the elements up
	to second power are closed under graded commutation. If the graduation
	is of type Z2 the elements of second power are a Lie-graded algebra
	and this is the only graduation for which this is true. The graded
	commutation relations of this algebra are calculated. It is isomorphic
	to the graded symplectic algebra of (V,{,}) which is contained in
	the graded derivation algebra of the graded Heisenberg algebra of
	elements up to first power.},
  doi = {DOI: 10.1016/0022-4049(77)90019-6},
  file = {:D\:\\eBooks\\papers\\representation\\hans Tilgner, graded generalizations of weyl- and clifford algebras.PDF:PDF},
  issn = {0022-4049},
  url = {http://www.sciencedirect.com/science/article/B6V0K-45FC361-31/2/5c75bdf9701c9e758f265f975d6e451e}
}

@ARTICLE{1976,
  author = {Ton-That, Tuong},
  title = {Lie Group Representations and Harmonic Polynomials of a Matrix Variable},
  journal = {Transactions of the American Mathematical Society},
  year = {1976},
  volume = {216},
  pages = {1--46},
  abstract = {The first part of this paper deals with problems concerning the symmetric
	algebra of complex-valued polynomial functions on the complex vector
	space of n by k matrices. In this context, a generalization of the
	so-called "classical separation of variables theorem" for the symmetric
	algebra is obtained. The second part is devoted to the study of certain
	linear representations, on the above linear space (the symmetric
	algebra) and its subspaces, of the complex general linear group of
	order k and of its subgroups, namely, the unitary group, and the
	real and complex special orthogonal groups. The results of the first
	part lead to generalizations of several well-known theorems in the
	theory of group representations. The above representation, of the
	real special orthogonal group, which arises from the right action
	of this group on the underlying vector space (of the symmetric algebra)
	of matrices, possesses interesting properties when restricted to
	the Stiefel manifold. The latter is defined as the orbit (under the
	action of the real special orthogonal group) of the n by k matrix
	formed by the first n row vectors of the canonical basis of the k-dimensional
	real Euclidean space. Thus the last part of this paper is involved
	with questions in harmonic analysis on this Stiefel manifold. In
	particular, an interesting orthogonal decomposition of the complex
	Hilbert space consisting of all square-integrable functions on the
	Stiefel manifold is also obtained.},
  copyright = {Copyright 1976 American Mathematical Society},
  file = {:D\:\\eBooks\\papers\\representation\\tuong ton-that, Lie Group Representations and Harmonic Polynomials of a Matrix Variable.PDF:PDF},
  issn = {00029947},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Feb., 1976},
  publisher = {American Mathematical Society},
  url = {http://www.jstor.org/stable/1997683}
}

@ARTICLE{vergne1geometric,
  author = {Mich\`ele Vergne},
  title = {Geometric quantization and equivariant cohomology},
  volume = {1},
  pages = {249--295},
  booktitle = {First European Congress in Mathematics},
  file = {:D\:\\eBooks\\papers\\representation\\Vergne, Geometric quantization and equivariant cohomology.PDF:PDF}
}

@ARTICLE{vergne2006all,
  author = {Vergne, M.},
  title = {{All what I wanted to know about Langlands program and was afraid
	to ask}},
  journal = {Arxiv preprint math/0607479},
  year = {2006}
}

@ARTICLE{vergne1982representations,
  author = {Vergne, M.},
  title = {Representations of Lie groups and the orbit method},
  journal = {Lecture notes from talk given in honor of Emmy Noether's 100th birthday},
  year = {1982},
  file = {:D\:\\eBooks\\papers\\representation\\Vergne, Representations of Lie groups and the orbit method.pdf:PDF}
}

@INCOLLECTION{Vogan2000,
  author = {David A. Vogan},
  title = {The method of coadjoint orbits for real reductive groups},
  booktitle = {Representation Theory of Lie Groups},
  publisher = {AMS and IAS/Park City Mathematics Institute},
  year = {2000},
  editor = {Jeffrey Adams and David Vogan},
  volume = {8},
  series = {IAS/Park City Mathematics Series},
  file = {:D\:\\eBooks\\papers\\representation\\David A. Vogan, The method of coadjoint orbits for real reductive groups.pdf:PDF},
  owner = {hoxide},
  timestamp = {2010.03.04}
}

@ARTICLE{Vogan98alanglands,
  author = {David A. Vogan},
  title = {A Langlands classification for unitary representations},
  year = {1998},
  file = {:D\:\\eBooks\\papers\\representation\\David Vogan,A Langlands classification for unitary representations.PDF:PDF}
}

@ARTICLE{Vogan1989Var,
  author = {David A.jun. Vogan},
  title = {Associated varieties and unipotent representations.},
  year = {1991},
  abstract = {{Let $G_0$ be a connected real semisimple Lie group with finite center
	and Lie algebra ${\germ g}_0$. Let $K_0$ and ${\germ k}_0$ be a maximal
	compact subgroup of $G_0$ and its Lie algebra, respectively. To any
	admissible representation $\pi$ of $G_0$ one attaches its Harish-Chandra
	module $X$ of $K_0$-finite vectors, which carries an algebraic action
	of the complexification $K$ of $K_0$ and a (compatible) Lie algebra
	representation of the complexification $\germ g$ of ${\germ g}_0$.
	If $\pi$ is of finite length, then $X$ is finitely generated over
	the enveloping algebra $U$ of $\germ g$. In this case, given any
	good filtration of the $U$-module $X$ by $K$-invariant subspaces,
	the associated graded module $\text {gr }X$ is finitely generated
	over $\text{gr } U = S({\germ g})$. Since the ideal generated by
	$\germ k$ in $S({\germ g})$ annihilates $\text {gr }X$, we can view
	the latter as a finitely generated $S({\germ g}/{\germ k})$-module.
	The zero set of its annihilator is called the associated variety
	$\cal V$ of $X$; it is a $K$-stable subvariety of $({\germ g}/{\germ
	k})^*$. Using the Killing form and a complexified Cartan decomposition
	${\germ g} = {\germ k} + {\germ p}$ of ${\germ g}_0$, we may identify
	$\cal V$ with a $K$-stable subvariety of the cone ${\cal N}$ of nilpotent
	elements in $\germ p$. By results of {\it B. Kostant} and {\it S.
	Rallis} [Am. J. Math. 93, 753-809 (1971; Zbl 0224.22013)], $\cal
	N$ has only finitely many $K$-orbits, whence so too does $\cal V$.
	By results of {\it J. Sekiguchi} [J. Math. Soc. Japan 39, 127-138
	(1987; Zbl 0627.22008)], the orbits of $K$ in $\germ p$ stand in
	1-1 correspondence with nilpotent $G_0$ orbits in ${\germ g}_0$.
	Thus one may pass from representations of $G_0$ to nilpotent orbits.
	The method of coadjoint orbits attempts to proceed in the opposite
	direction, from nilpotent orbits to representations. The (as yet
	undefined) representations so obtained are called unipotent. -- The
	author discusses a number of partial results and tantalizing conjectures
	relating irreducible Harish- Chandra modules to their associated
	varieties. The results and conjectures are motivated and inspired
	by the orbit method mentioned above.}},
  classmath = {{*22E46 (Semi-simple Lie groups and their representations) 22E47 (Repres.
	of Lie and real algebraic groups: algebraic methods) }},
  howpublished = {{Harmonic analysis on reductive groups, Proc. Conf., Brunswick/ME
	(USA) 1989, Prog. Math. 101, 315-388 (1991).}},
  keywords = {{associated variety; unipotent representation; nilpotent orbit; Sekiguchi
	correspondence; connected real semisimple Lie group; admissible representation;
	Harish-Chandra module; Killing form; Cartan decomposition}},
  language = {English},
  reviewer = {{W.M.McGovern (Seattle)}}
}

@ARTICLE{Vogan1979a,
  author = {Vogan, David A.},
  title = {A generalized $\tau$-invariant for the primitive spectrum of a semisimple
	Lie algebra},
  journal = {Mathematische Annalen},
  year = {1979},
  volume = {242},
  pages = {209--224},
  number = {3},
  month = oct,
  file = {:D\:\\eBooks\\papers\\representation\\David A. vogan, A generalized tau-invariant for the primitive spectrum of a semisimple Lie algebra.pdf:PDF},
  owner = {hoxide},
  timestamp = {2010.04.29},
  url = {http://dx.doi.org/10.1007/BF01420727}
}

@ARTICLE{Vogan1978,
  author = {Vogan, David A.},
  title = {Gelfand-Kirillov dimension for Harish-Chandra modules},
  journal = {Inventiones Mathematicae},
  year = {1978},
  volume = {48},
  pages = {75--98},
  number = {1},
  month = {feb},
  file = {:D\:\\eBooks\\papers\\representation\\David A. Vogan,Gelfand-Kirillov dimension for Harish-Chandra modules.pdf:PDF},
  owner = {hoxide},
  timestamp = {2009.05.30},
  url = {http://dx.doi.org/10.1007/BF01390063}
}

@ARTICLE{VoganZuckerman1984,
  author = {Vogan, David A. and Zuckerman, Gregg J.},
  title = {Unitary representations with nonzero cohomology.},
  journal = {Compos. Math. },
  year = {1984},
  volume = {53},
  pages = {51-90},
  abstract = {{An important problem in the theory of automorphic forms is to compute
	cohomology of locally symmetric spaces. Matsushima's formula [{\it
	A. Borel} and {\it N. R. Wallach}, Continuous cohomology, discrete
	subgroups, and representations of reductive groups (1980; Zbl 0443.22010),
	see p. 223] relates this problem to computations of cohomology of
	infinite-dimensional representations of the corresponding semisimple
	group. More precisely, the problem is the following: Suppose G is
	a reductive Lie group with Lie algebra ${\frak g}$ and maximal compact
	subgroup K. Find all unitary irreducible representations $\pi$ such
	that (*) $H\sp*({\frak g},K,\pi)\ne 0$ or more generally $H\sp*({\frak
	g},K,\pi \otimes F)\ne 0$ where F is finite-dimensional. \par The
	paper under review describes all Harish-Chandra modules satisfying
	(*). The results are sharp in the sense that $\pi$ and $H\sp*({\frak
	g},K,\pi \otimes F)$ are very explicit. The representation $\pi$
	is obtained by what is known as the ``derived functors construction''
	from a 1-dimensional unitary character on a Levi subgroup. Their
	unitarity is only conjectured (established later by {\it D. Vogan}
	[Ann. Math., II. Ser. 120, 141--187 (1984; Zbl 0561.22010)]). The
	techniques involve the Dirac inequality and its consequences obtained
	by {\it S. Kumaresan} [Invent. Math. 59, 1--11 (1980; Zbl 0442.22010)]
	and the classification of Harish-Chandra modules as in {\it D. Vogan}'s
	book [Representations of real reductive Lie groups (1981; Zbl 0469.22012)].
	Several consequences are described, such as a vanishing theorem for
	cohomology.}},
  classmath = {{*22E46 (Semi-simple Lie groups and their representations) 22E47 (Repres.
	of Lie and real algebraic groups: algebraic methods) 11F70 (Representation-theoretic
	methods in automorphic theory) 32N10 (Automorphic forms of several
	complex variables) 11F67 (Special values of automorphic L-series,
	etc) }},
  file = {:D\:\\eBooks\\papers\\representation\\Vogan, David A.jun, Zuckerman, Gregg J., Unitary representations with nonzero cohomology.djvu:Djvu},
  keywords = {{automorphic forms; cohomology of locally symmetric spaces; infinite-
	dimensional representations; semisimple group; reductive Lie group;
	Lie algebra; unitary irreducible representations; Harish-Chandra
	modules; vanishing theorem for cohomology}},
  language = {English},
  reviewer = {{D. Barbasch (MR 86k:22040)}}
}

@ARTICLE{Vogan1984,
  author = {Vogan, David A., Jr.},
  title = {Unitarizability of Certain Series of Representations},
  journal = {The Annals of Mathematics},
  year = {1984},
  volume = {120},
  pages = {141--187},
  number = {1},
  copyright = {Copyright 漏 1984 Annals of Mathematics},
  file = {:D\:\\eBooks\\papers\\representation\\David A. Vogan, Unitarizability of Certain Series of Representations.pdf:PDF},
  issn = {0003486X},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Jul., 1984},
  publisher = {Annals of Mathematics},
  series = {Second Series},
  url = {http://www.jstor.org/stable/2007074}
}

@ARTICLE{Vogan1979,
  author = {Vogan, David A., Jr.},
  title = {The Algebraic Structure of the Representations of Semisimple Lie
	Groups I},
  journal = {The Annals of Mathematics},
  year = {1979},
  volume = {109},
  pages = {1--60},
  number = {1},
  copyright = {Copyright 1979 Annals of Mathematics},
  file = {:D\:\\eBooks\\papers\\representation\\David A. vogan, The Algebraic Structure of the Representations of Semisimple Lie Groups I.pdf:PDF},
  issn = {0003486X},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Jan., 1979},
  publisher = {Annals of Mathematics},
  series = {Second Series},
  url = {http://www.jstor.org/stable/1971266}
}

@ARTICLE{WallachZhu2004,
  author = {N.R. Wallach and C.B. Zhu},
  title = {Transfer of unitary representations},
  journal = {Asian Journal of Mathematics},
  year = {2004},
  volume = {8},
  pages = {861--880},
  number = {4},
  file = {:D\:\\eBooks\\papers\\representation\\Nolan R. Wallach, Chen-bo Zhu,transfer of unitary representations.pdf:PDF}
}

@BOOK{Wallach1992real,
  title = {Real reductive groups II},
  publisher = {Academic Press},
  year = {1992},
  author = {Nolan R. Wallach},
  volume = {132},
  pages = {448},
  series = {Pure and Applied Mathematics},
  file = {:E\:\\mathbook\\Classified\\representation\\Real reductive groups II.pdf:PDF}
}

@BOOK{Wallach1988,
  title = {Real reductive groups I},
  publisher = {Academic Press, Inc., Boston},
  year = {1988},
  author = {Nolan R. Wallach},
  volume = {132},
  pages = {412},
  series = {Pure and applied mathematics},
  file = {:E\:\\mathbook\\Classified\\representation\\Real reductive groups I.pdf:PDF},
  owner = {hoxide},
  timestamp = {2009.03.24},
  url = {http://www.ams.org/mathscinet-getitem?mr=929683}
}

@ARTICLE{Wallach1984,
  author = {Wallach, Nolan R.},
  title = {On the unitarizability of derived functor modules},
  journal = {Inventiones Mathematicae},
  year = {1984},
  volume = {78},
  pages = {131--141},
  number = {1},
  month = feb,
  file = {:D\:\\eBooks\\math\\papers\\representations\\Wallach\\On the unitarizability of derived functor modules..pdf:PDF},
  owner = {hoxide},
  timestamp = {2009.03.24},
  url = {http://dx.doi.org/10.1007/BF01388720}
}

@ARTICLE{Wallach1979I,
  author = {Wallach, Nolan R.},
  title = {The Analytic Continuation of the Discrete Series.I},
  journal = {Transactions of the American Mathematical Society},
  year = {1979},
  volume = {251},
  pages = {1--17},
  abstract = {In this paper the analytic continuation of the holomorphic discrete
	series is defined. The most elementary properties of these representations
	are developed. The study of when these representations are unitary
	is begun.},
  copyright = {Copyright © 1979 American Mathematical Society},
  file = {:D\:\\eBooks\\papers\\representation\\Nolan R. Wallach, The Analytic Continuation of the Discrete Series I.pdf:PDF},
  issn = {00029947},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Jul., 1979},
  publisher = {American Mathematical Society},
  url = {http://www.jstor.org/stable/1998680}
}

@ARTICLE{Wallach1979II,
  author = {Wallach, Nolan R.},
  title = {The Analytic Continuation of the Discrete Series. II},
  journal = {Transactions of the American Mathematical Society},
  year = {1979},
  volume = {251},
  pages = {19--37},
  abstract = {This is the second in a series of papers on the analytic continuation
	of the holomorphic discrete series. In this paper necessary and sufficient
	conditions for unitarizability are given in the case of line bundles.
	The foundations for the vector valued case are begun.},
  copyright = {Copyright 1979 American Mathematical Society},
  file = {:D\:\\eBooks\\papers\\representation\\Nolan R. Wallach, The Analytic Continuation of the Discrete Series II.pdf:PDF},
  issn = {00029947},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Jul., 1979},
  publisher = {American Mathematical Society},
  url = {http://www.jstor.org/stable/1998681}
}

@ARTICLE{WallachNolan1976,
  author = {Wallach, Nolan R.},
  title = {On the Enright-Varadarajan modules: a construction of the discrete
	series},
  journal = {Ann. Sci. Ecole Norm. Sup. (4)},
  year = {1976},
  volume = {9},
  pages = {81--101},
  number = {1},
  file = {:D\:\\eBooks\\math\\papers\\representations\\Wallach\\On the Enright-Varadarajan modules a construction of the discrete series.djvu:Djvu},
  owner = {hoxide},
  timestamp = {2009.05.19}
}

@ARTICLE{1971,
  author = {Wallach, Nolan R.},
  title = {Cyclic Vectors and Irreducibility for Principal Series Representations},
  journal = {Transactions of the American Mathematical Society},
  year = {1971},
  volume = {158},
  pages = {107--113},
  number = {1},
  abstract = {Canonical sets of cyclic vectors for principal series representations
	of semisimple Lie groups having faithful representations are found.
	These cyclic vectors are used to obtain estimates for the number
	of irreducible subrepresentations of a principal series representations.
	The results are used to prove irreducibility for the full principal
	series of complex semisimple Lie groups and for $SL(2n + 1, R), n
	\geqq 1$.},
  copyright = {Copyright 1971 American Mathematical Society},
  issn = {00029947},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Jul., 1971},
  publisher = {American Mathematical Society},
  url = {http://www.jstor.org/stable/1995774}
}

@ARTICLE{Wallach1969,
  author = {Wallach, Nolan R.},
  title = {Induced Representations of Lie Algebras. II},
  journal = {Proceedings of the American Mathematical Society},
  year = {1969},
  volume = {21},
  pages = {161--166},
  number = {1},
  copyright = {Copyright 1969 American Mathematical Society},
  file = {:D\:\\eBooks\\papers\\representation\\N.R. Wallach, Induced Representations of Lie Algebras. II.pdf:PDF},
  issn = {00029939},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Apr., 1969},
  publisher = {American Mathematical Society},
  url = {http://www.jstor.org/stable/2036882}
}

@ARTICLE{Weil1965,
  author = {Weil, Andr\'e},
  title = {Sur la formule de Siegel dans la th\'eorie des groupes classiques},
  journal = {Acta Mathematica},
  year = {1965},
  volume = {113},
  pages = {1-87},
  note = {10.1007/BF02391774},
  affiliation = {The Institute for Advanced Study Princeton N.J. USA Princeton N.J.
	USA},
  file = {:D\:\\eBooks\\papers\\representation\\Weil, Sur la formule de Siegel dans la theorie des groupes classiques.PDF:PDF},
  issn = {0001-5962},
  issue = {1},
  keyword = {Mathematics and Statistics},
  publisher = {Springer Netherlands},
  url = {http://dx.doi.org/10.1007/BF02391774}
}

@ARTICLE{Weil1964,
  author = {Weil, Andre},
  title = {Sur certains groupes d'operateurs unitaires},
  journal = {Acta Mathematica},
  year = {1964},
  volume = {111},
  pages = {143--211},
  number = {1},
  month = jul,
  abstract = {Sans rsum},
  file = {:D\:\\eBooks\\papers\\representation\\Andre Weil,Sur certains groupes d'operateurs unitaires.pdf:PDF},
  owner = {hoxide},
  timestamp = {2010.05.30},
  url = {http://dx.doi.org/10.1007/BF02391012}
}

@ARTICLE{ZhuHuang1997,
  author = {Chenbo Zhu and JingSong Huang},
  title = {On certain small representations of indefinite orthogonal groups},
  journal = {Represent. Theory},
  year = {1997},
  volume = {1},
  pages = {190-206},
  file = {:D\:\\eBooks\\papers\\representation\\chenbo zhu and jingsong huang, On certain small representations of indefinite orthogonal groups.pdf:PDF},
  owner = {hoxide},
  timestamp = {2010.02.08}
}

@ARTICLE{Zhu2003,
  author = {Chen-Bo Zhu},
  title = {Representations with scalar K-types and applications},
  journal = {Israel Journal of Mathematics},
  year = {2003},
  volume = {135},
  pages = {111--124},
  number = {1},
  month = dec,
  abstract = {Abstract&nbsp;&nbsp;We discuss some results of Shimura on invariant
	differential operators and extend a folklore theorem about spherical
	representationas to representations with scalarK-types. We then apply
	the result to obtain non-trivial isomorphisms of certain representations
	arising from local theta correspondence, many of which are unipotent
	in the sense of Vogan.},
  file = {:D\:\\eBooks\\papers\\representation\\Zhu Chen-bo, Representations with scalar K-Types and applications.PDF:PDF},
  owner = {hoxide},
  timestamp = {2009.08.27},
  url = {http://dx.doi.org/10.1007/BF02776052}
}

@ARTICLE{Zhu1992,
  author = {Zhu, Chen-Bo},
  title = {Invariant distributions of classical groups.},
  journal = {Duke Math. J. },
  year = {1992},
  volume = {65},
  pages = {85-119},
  number = {1},
  abstract = {{Let $G$ be a classical group over $\bbfR$ (orthogonal, unitary etc.)
	and $V$ the space of its standard representation. The $G$-invariant
	tempered distributions on $V\sp k$ are studied by the following method.
	One defines an appropriate symplectic form on $W=V\sp{2k}$ such that
	$G$ is part of a dual pair $(G,G')$ in $Sp(W)$. We then have the
	oscillator representation of the 2-fold cover $\widetilde Sp(W)$
	of $Sp(W)$ and $\widetilde G'$ acts on the space $S$ of $G$-invariant
	tempered distributions on $V\sp k$. Now the irreducible representations
	of a maximal compact subgroup of $\widetilde G'$ which occur in $S$
	are determined, and their multiplicity is proved to be one. Also,
	an embedding of $S$ into the space of generalized functions on a
	representation space of $\widetilde G'$ (induced from a character
	of a parabolic subgroup) is constructed.}},
  classmath = {{*22E45 (Analytic repres.of Lie and linear algebraic groups over real
	fields) 46F10 (Operations with distributions (generalized functions))
	}},
  doi = {10.1215/S0012-7094-92-06504-5},
  file = {:D\:\\eBooks\\papers\\representation\\Zhu Chengbo, Invariant distributions of classical groups.pdf:PDF},
  keywords = {{standard representation; $G$-invariant tempered distributions; symplectic
	form; dual pair; oscillator representation; irreducible representations;
	maximal compact subgroup; multiplicity}},
  language = {English},
  reviewer = {{J.G.M.Mars (Utrecht)}}
}

@ARTICLE{Zuckerman1977,
  author = {Zuckerman, Gregg},
  title = {Tensor Products of Finite and Infinite Dimensional Representations
	of Semisimple Lie Groups},
  journal = {The Annals of Mathematics},
  year = {1977},
  volume = {106},
  pages = {295--308},
  number = {2},
  copyright = {Copyright 1977 Annals of Mathematics},
  file = {:D\:\\eBooks\\papers\\representation\\Zuckerman, Tensor Products of Finite and Infinite Dimensional Representations.PDF:PDF},
  issn = {0003486X},
  jstor_articletype = {primary_article},
  jstor_formatteddate = {Sep., 1977},
  publisher = {Annals of Mathematics},
  series = {Second Series},
  url = {http://www.jstor.org/stable/1971097}
}

